## Pages

### IITJEE Study Material:Elasticity

-Elasticity is the property of material body to regain its original condition on removal of deforming forces.
-Bodies which can recover their original condition on removal of deforming forces are perfectly elastic bodies .
-Bodies which does not have tendency to recover their original condition on removal of deforming forces are called plastic bodies.
-There are no perfectly elastic or plastic bodies and actual bodies lie between two extremes.
(1) STRESS
-Stress is the restoring force per unit area set up inside the body and is measured by the magnitude of deforming force acting on unit area of the body within the elastic limits of the body.
Magnitude of stress=F/A where, Fis the force applied and A is the area of crosssection of the body.
-S.I. unit of sterss is N/m2.-Dimensional formula of stress is[ML1T-2].
(A) Normal Stress:- If elastic forces developed are perpandicular to the area of cross-section of the body then the stress developed is known as normal stress.
(B) Tangential Stress:- Tangential or shearing stress developes in a body when elastic restoring forces are parallel to the cross-sectional area of the body and the body gets sheared through a certain angle.
(2) STRAIN
-When a body is under a system of forces or couples in equilibrium then a change is produced in dimensions of the body and this fractional change produced in the body is called Strain.
(A) longitudinal strain=Δl/l, where l is the original length and Δl is the change in length.
(B) volume strain=ΔV/V, where V is the original volume and ΔV is the change in volume.
(C) if the deforming forces produces change in shape of the body then the strain is called shearing strain.
-Strain is an dimensionless quantity.
(3)HOOK'S LAW
-Hook's law states that 'For small deformations, within elastic limits, stress is directly proportional to strain'.
Thus, stress ∝ strain
or, stress/strain=constant-This constant is known as modulus of elasticity of given material.
(4)MODULUS OF ELASTICITY
(A) Young's modulus of elasticity:-
-Young's modulus of elasticity is given by
Y=longitudinal Stress/longitudinal Stress
= (F/A)/(Δl/l)
=Fl/AΔl
-It has dimensions of pressure.
(B) Bulk modulus of elasticity:-
-Bulk modulus of elasticity is the ratio of normal stress to volume strain within elastic limits.
-It is denoted by k and
K=FV/AΔV
(C) Modulus of rigidity:-
-When a body is sheared , the ratio of tangential stress to the shearing strain within elastic limits is called modulus of rigidity.

### Physics for IITJEE: QuestionBank-1 (E-book)

A Great offer for Students

Physics has been one of the toughest subject for the students of 11th,12th class and students preparing for Competitive examinations.Student face lots of problems in this area.They got stuck on a problem and dont find way to get out of it.They got tired of cramming solution and seek better understanding of the subject.They have to purchase lot of books to get various type of problems which involve high cost.They are quite nervous about homework and Examination.

We are presenting our Second package Physics-QuestionBank-1 which includes complete solution for all the problems given in the blog plus 50 new problems.This Package will provide you lots of problems along with their step by step detailed solutions at a very low cost.Besides this we are also providing other short stuff like examination tips,biograhies,quick recap ,Physics Calculators ,Units Converters and many more.

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• Detailed Solutions to all the 400 Question(Subjective/Objective) given in the Blog
• 50 More problems spanning all the Units
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• Biographies
• IIT And AIEEE Full Syllabus
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### Physics for IITJEE:Objective Questions

1. In an SHM,x is displacement and y is acceleration at time t.The curve of y agianst x for one complete oscillation will be
a. An ellipse
b. A circle
c. A straight line
d. A sinusoidal curve

2.At 0° C a body emits
b. All wavelenghts
c. only visible light

3.A person 6 feet in height can see his full size erect image in a mirror 2 feet in height.This mirror has to be
a. plane or convex
b plane or concave
c. Necessarly convex
d. Necessarly concave

4. A parallel plate capacitor is made by stacking m equally spaced plates connect alternately.If the Capacitance between any two plates is C.Then the resultant capacitance is
a. C
b. mC
c.(m+1)C
d (m-1)C

5.The radioacativity of a sample is R1 at time t1 and R2 at time t2.Mean life of the specimen is T.The numbers of atoms that have disintegrated is the time interval(t2-t1)
a. R1t1-R2t2
b.R1-R2
c.(R1-R2)/T
d..(R1-R2)T

### Physics for IITJEE: Detailed Solutions

Hello Friends

We have been continuously updating the blog of lots of questions spanning various topics in physics. So far we have given around 600 questions in the blogs spanning various topics.
Till now we have been giving hints and answer to the questions given in the blog Now we have start adding the detailed solutions of few question in old post. So now you can get detailed solutions for free

I will be adding the detailed solutions in the post itself.Please check individual post for them

So far details solutions are added in Mechanics and Thermodynamics.Do check the details solutions

Index is given at the right hand side of the blog.You can click for thermodynamics and mechanics modules there.

### Problem Solving Corner

Hello Friends
We are pleased to anounce physics problem solving corner on this blog

You can send us your questions and queries ,we will try to solve them and publish them on this blog
Each month your 5 questions will be published with detailed solution.
All you need to do is mail us on following address to get the solution of your problems
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### Physics for IITJEE:Free Physics Ebook

We have developed few physics ebooks .The material in these books are quite good and you wont find it any where else

These Ebooks contains some good question spanning all the units.Detailed Solutions are also provided for that.
we have put in considerable work to write these e-books.
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### Physics for IITJEE:Heat and Thermodynamics Study Material

A Great offer for Students

Physics has been one of the toughest subject for the students of 11th,12th class and students preparing for Competitive examinations.Student face lots of problems in this area.They got stuck on a problem and dont find way to get out of it.They got tired of cramming solution and seek better understanding of the subject.They have to purchase lot of books to get various type of problems which involve high cost.They are quite nervous about homework and Examination.

We are proud to present our first package about the unit Heat and thermodynamics which includes complete solution for all these common faced problems.You will get good notes and lots of problems and their step by step detailed solutions at a very low cost.Besides that we also provide lot of other short stuff like examination tips,biograhies,quick recap and many other.

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This package includes following features

• Details Notes for all the chapter to clear your concepts

• Short Notes for quick Recap to revise at the time of any examination

• Chapter wise Questions with Detail Solutions in various format
-Multiple choice question with only one answer
-Multiple choice question with one or more answers
-Subjective Questions

• Miscllaneaous Question at the end of the units with Detailed solutions in various Format
-Assertion Reasson questions
-Matrix Type question
-Multiple choice question with only one answer
-Multiple choice question with one or more answer
-Subjective Questions
-Fill in the blanks
-True and False

• Difficulity Level matches that of IITJEE/AIEEE

• Biographies of all the Author of Heat And Thermodynamics

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• It contains around 200 Solved problems

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### Physics for IITJEE:Optics Short Notes-1

Agenda :Summary of the basics of Optics

Reflection of light
-When light travelling in one medium is incident on a second medium some part of it is sent back to the first medium according to some definite laws and is said to be reflected.
-In practice mirrors are used to reflect light.
-The angle which the incident ray and the reflected ray make with normal to the surface are termed as Angles of incidence and of reflection respectively.

Laws of reflection:-
Law 1- The incident ray, the reflected ray and the normal to the surface , all lie in the same plane.
Law 2- The angle of incidence i is equal to the angle of reflection r.

Spherical Mirrors :-
Assuming that all the reflecting surfaces are portions of a sphere, if the inside surface reflects, the mirror is concave and if the outside surface which reflects, it is convex as shown below in the figure.
-Relation between focal length f and radius of curvature R of the mirror is
f=R/2
and both f and R are taken as positive for concave mirror and negative for convex mirror.
-Mirror formula is the relation between distance of the object (u), distance of the image (v) and the focal length (f) of the mirror and is,
(1/u)+(1/v)=(1/f)
-Mirror formula holds for a spherical mirror of small aperture only.
-The ratio of size of the image formed (by spherical mirror) to the size of the object is called magnification. Mathematically,
m=I/O
=-v/u
-Spherical abberation is the inability of a spherical mirror of large aperture to bring all the rays of wide beam of light falling

on it to focus at a single point.

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### Winner of Physics Champion Contest -2

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We receive lot of entries for the contest.Thanks all for the Response

1. c
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3.b,c
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5.a

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### IITJEE PHYSICS:Current Electricity Part -I

Agenda: Summary of Current Electricity

-A current flows along a metal or wire when battery is connected to it.
-Current in a wire is due to free electrons moving along the wire
-The Battery has a Potential difference between its poles due to chemical changes inside the battery.The Potential difference pushes the electrons alongs the metal.The Potential diffrence between the terminal is call the EMF of the battery.
-One pole of the battery is called positive pole and another one is call the negative pole.
-Current direction is opposite to the electron flow direction.
-EMF is measured in Volt

Electric current is defined as the rate at which charge flows inside the conductor
so
I=Q/t
- Its unit is Amphere
Also I=dQ/dt

Drift speed of electrons inside the conductor
vd=I/neA
Where I is the current,n is the number of the electron per unit volume ,e is the electronic charge and A is the area of the crossection of the conductor

Ohms Law

V=IR
where V is the Potential difference accross its ends
I is the current flow
And R is the electrical Resistance of the conductor.Electrical Resistance unit is Ohm

ELectrical Resistivity

It is defined as
ρ=RA/L

Where R is the Resistance
A is the crossectional Area
L is the length

Series Resistors

R=R1+R2+R3

Parallel Resistors

(1/R)=(1/R1)+(1/R2)+(1/R2)

Terminal Voltage of the Cell

V=E-Ir

where E is the EMF of the cell and r is the internal resistance of the Cell

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### Physics for IITJEE:Exercise your Brain with Miscellaneous Physics Question

Question 1:
A 2 kg body moving to the right with speed 6 m/s coliides elastcally with a stationary body of mass 4 kg.
a.Find the velocity vector of each mass relative to center of mass before and after the collsion
b.Find the velocity vector of the each mass in original frame after the collision
c.How much energy was transfered to the 4 kg body.

Take i as the unit vector in the right direction

a.
Before collision
Velocity vector of mass 2 kg=4i m/s
Velocity vector of mass 4 kg=-2i m/s

After collision
Velocity vector of mass 2 kg=-4i m/s
Velocity vector of mass 4 kg=2i m/s

b
Velocity vector of mass 2 kg=-2i m/s
Velocity vector of mass 4 kg=4i m/s

c. 32 J

Hints:
Velocity of the center of mass=m1v1+m2v2/m1+m2
Velocity w.r.t CM=v-vcm

Applying law of linear momentum and energy conservation,veloclities after collosion could be find out

Question 2:
A small solid cylinder of radius r rolls down from the top of sphere of Radius R without slipping.
a. find the angle made from the vertical at which the cylinder loses contact with the surface of the sphere
b.find the angular velocity of the cylinder at the moment it loses contact with the surface of the sphere

a. cos-1(4/7)
b.(2/r)[(R+r)g/7]1/2

hints:

Normal reaction will become zero at the point of losing contact
so centripetal force will become equal to the weight components across the radius.
Also applying law of conservation of energy ...we can find the solution

Question 3:

An gas obeys Vander waal equation

(P+a/V2)(V-b)=nRT

Find following for such a gas

A. The dimensional formula for constant a is
a.ML5T-2
b.ML5T-1
c.ML-1T-1
d. M0L-0T0

B. Find the workdone by this gas when gas expand from V to 2V at constant temperature T
a.nRTloge(2V-b/V-b) -a/V
b.nRTloge(2V-b/V-b) +a/V
c. nRTloge(2V-b/V-b)
d. none of the above

C.Bulk modulus at constant pressure is defined as
K=(-1/V)(dP/dV)T
Find the value of k for this gas
a.(1-b/V)(p-a/V2+2a/V3)
b. (1+b/V)(p-a/V2+2a/V3)
c.(1-b/V)(p-a/V2-2a/V3)
d.None of the above

A.ML5T-2
B.nRTloge(2V-b/V-b) -a/V

Question 4:
An electron (mass m and charge e) is moving along the axis of the ring of radius r and carrying a charge q.Find the time period of small oscillation of the electron about the center of the ring

T=4π(πε0mr3/eq)1/2

Hint:
Electric field at a point on the axis of the ring at the distance x from its center is
E=qx/4πε0(r2+x2)3/2

### IITJEE Test series 2 (Modern Physics)

(A) Multiple choice questions with one answer
1. The ionizing power of the radiations are in the increasing order of
(a) γ,β ,α
(b) α , β,γ
(c) α , γ,β
(d) β, γ,α

2.A photon of energy 5.0 eV imparts all it's energy to an electron that leaves a metal surface with 1.5 eV of kinetic energy.The work function α of metal would be
(a) 6.5 eV
(b) 3.5 eV
(c) 3.9 eV
(d) 1.5 eV

3. A thermal neutron of mass 1.67× 10-27 Kg is travelling at a speed of 2500 m/s. de Brogli wavelength of thermal neutron is
(a) 1.4 × 10-10m
(b) 12 × 10-10m
(c) 1.6 × 10-10m
(d) 1.0 × 10-10m

4. Uncertainity in the position of a particle is equal to twice its de Brogli wavelength. Uncertainity in its velocity would be
(a) Δvx≥(1/4π)vx
(b) Δvx≥(1/π)vx
(c) Δvx≥(1/2π)vx
(d) Δvx≥(1/8π)vx

5. The shortest wavelength of X-Rays emitted from an X-Ray tube depends upon
(a) atomic number of target material
(b) current in the tube
(c) voltage applied to the tube
(d) nature of gas in the tube

6. The largest wavelength present in the Balmer series of hydrogen atom is
(a) 656 nm
(b) 500 nm
(c) 600 nm
(d) 756 nm

(B) Matrix match type
Match the list P with the list Q to name the series for quantum jump of electrons in hydrogen atom

list P
(a) n=2 to n=3
(b) n=3 to n=4
(c) n=4 to n=5
(d) n=5 to n=6

list Q
1. Balmer
2. lyman
3. Paschen
4. Brackett
5. Pfund

(A) Multiple choice questions with one answer
1. a
2. b
3. c
4. d
5. c
6. d

(B) Matrix match type
a-2
b-1
c-3
d-4

### Modern Physics Test Series

(A) Multple choice questions

1. Photoelectric emission takes place when
(a)electrons falls on photosensitive surface
(b)alpha particles falls on photosensitive surface
(c)light rays falls on photosensitive surface
(d)neutrons falls on photosensitive surface

2. The velocity of most energetic photo electrons emitted from metal surface depends on
(a) time for which radiation fall on metal surface
(b) the frequency of incident light
(c) the intensity of incident light
(d) none of the above

3. The work funcion of a metal is w and λ is the wavelength of incident radiation. there would be no emission of photoelectrons when
(a) λ > hc/w
(b) λ < hc/w
(c) λ = hc/w
(d) λ ≤ hc/w

4. The fact that was not inferred from the Rutherford model of the atom was that the
(a) nucleus occupied a small space inside the atom
(b) nucleus consisted of neutrons and protons
(c) electrons were outside the nucleus of the atom
(d) nucleus was dense in nature

5. A graph showing the energy of the photoelectron as a fuction of the frequency of the radiation for a given emitting surface is best represented as
(a)

(b)

(c)

(d)

(B) Matrix match type question
6. Match the items mentioned with those given in group (P) with those given in group (Q)

(P)
(a) The concept of nuclear atom was
established from the experiment on the
(b) Wave aspect of matter was confirmed by
(c) Bohr theory was successful in explaining
(d) Photons may cause

(Q)
(1) emission of electrons from the metal surface
(2) scattering of alpha particles by a gold foil
(3) diffraction of electrons by a crystal
(4) bright line spectra of hydrogen atom
(5) scattering of X-rays by electrons

1. (c)
2. (b)
3. (a)
4. (c)
5. (a)
6. a-2
b-3
c-4
d-1

### IITJEE PHYSICS: Mechanics

Mulitiple choice question with one or more answer

1. The motion of center of mass of a system of two particles is unaffected by their internal forces
a, irrespective of the actual direction of the internal forces
b,only if they are along the line joining the particles
c.only if they are obliquely inclined to the line joinng the particles
d. only if they are right angles to the line joining the particles

2.Two discs of moments of inertia I1 and I2 about their respective axis rotating with angular frequencies ω1 and ω2 respectively are brought into contact face to face with their axes of rotation coincident.Which of the following is true
a.The angular frequency of the composite disc is (I1ω1+I2ω2)/(I1+I2)
b.dL/dt is constant for the system
c.Moment of the inertia of the composite disc about the axis is I1+I2
d. None of these

3.Net force on a system of particles is zero from some interial frame.which of the following is correct
a.Center of mass acceleration is zero from that inertial frame
b. Net momentum is constant from that frame
c.Net momentum from the frame of Center of mass is zero and constant
d. KE of the system from center of mass frame may be constant

4.Three points masses each of mass m are placed at the corner of an equilateral triangle of side a.The moment of inertia of the system about an axis along one side of an triangle is
a.3ma2/4
b. ma2/4
c. ma2/2
d ma2/6

5. A solid sphere rolls without slipping with speed v and presses a spring of spring constant k.The compression in the spring will be
a.(2Mv2/3k)1/2
b.(2Mv2/5k)1/2
c.(5kv2/7M)1/2
d.(7Mv2/5k)1/2

6.A solid cylinder of mass M and radius R is being pulled along a horizontal surface on which its perform pure rolling by a horizontal force F applied at its center.which of the following is true
a.Angular acceleration of the cylinder about the axis passing through center of mass is 2F/3MR
b.Frictional force acting on the cylinder is F/3
c.Velocity of a point on the top of cylinder after 3 sec is 4P/M
d . None of these

7.A uniform chain of mass M and lenght L is held on a horizontal frictionless table with 1/k lenght hanging over the edge of the table.The workdone in pulling the chain up the table
a.MgL/k
b. MgL/2k
c. MgL/k2
d. MgL/2k2

Solutions

1.Ans a
2.Ans a,b,c
3.ans a,b,c,d
4.aNS A
6.ans a,b,c
7.ans d

### Current electricity test series

(A) Assertion reason type question.

(a) If both assertion and reason are true and reason is correct explaination of assertion.
(b) If both assertion and reason are true and reason is not correct explaination of assertion.
(c) Assertion is true but reason is false.
(d) both assertion and reason are false.

(1)
Assertion:Wire carrying current is not charged.
Reason:It is because , at any instant number of electrons leaving wire is sometimes equal to the number of electrons flowing in from the battery.

(2)
Assertion:Drift velocity of electrons decreases on increasing temperature of the conductor.
Reason:It is because, on increasing temperature of a conductor , the value of resistivity of it's material increases.

(3)
Assertion:Resistors are connected in series combination in order to increase the resistance of the circuit.
Reason:In series combination potential difference across any resistor is proportional to it's resistance.

(4)
Assertion:A potentiometer measures the potential difference more accurately then a voltmeter.
Reason:Because it has a wire of high resistance and draws a heavy current from external circuit.

(B) Multiple choice questions with only one answer

(5) A constant voltage is applied between the two ends of a uniform metalic wire and some heat is developed in it . The heat developed is doubled if,
(a) both length and radius of wire are halved
(b) both length and radius of wire are doubled
(c) radius of wire is doubled
(d) length of wire is doubled

(6) Kirchoff's first law of electric circuits is based on the law of conservation of
(a) only on mass
(b) only on charge
(c) on charge as well as on energy
(d) on charge as well as on mass

(7)The temperature coefficent of resistance of wire is 0.00125°C-1. At 300K, it's resistance is 1 ohm. The resistance of wire would be 2 ohm at
(a) 1154K
(b) 1127K
(c) 1167K
(d) 1176K

(8) If the length of the potentiometer wire is increased, then the accuracy in determination of null point
(a) will increase
(b) will decrease
(c) will remain unaffected
(d) can not be decided , untill emf of auxiliary battery is known

(9) Each of the resistance in the network shown in the figure is equal to R. The resistance between terminal A and B is

(a) R
(b) 5R
(c) 3R
(d) 6R

(10)The current voltage graph for a given metallic wire at two different temperatures T1 and T2 are shown in the fig. which one of the following option is true

(a) T1 = T2
(b) T1 < T2
(c) T1 > T2
(d) none of the above

Solutions
1.c
2.a
3.b
4.c
5.b
6.b
7.b
8.a
9.a
10.b

### Rotation Objective Test

1. A mass is whirled in a circular path with constant angular velocity and its angular momentum is L.If the string is now halve keeping the angular velocity same then angular momentum is
a. L
b. L/4
c. L/2
d. 2L

2.A mass is moving with constant velocity along a line parallel to xaxis away from origin.its angular momentum with respect to origin is
a. is zero
b. remains constant
c. goes on increasing
d. goes on decreasing

3.A cylinder rolls up the incline plane reaches some height and then roll down without slipping through out this section.The direction of the frictional force acting on the cylinder are
a. Up the incline while ascending and down the incline while descending
b.Up the incline while ascending and desending
c. down the incline while ascending and up the incline while descending
d.down the incline while ascending and desending

4.A uniform sold sphere rolls on the horizontal surface at 20 m/s.it then rolls up the incline of 30.If friction losses are negligible what will be the value of h where sphere stops on the incline
a. 28.6 m
b 30 m
c. 28 m
d. none of these

5 A cylinder of Mass M and radius R rolls down a incline plane of inclination θ.Find the linear accleration of the cylinder
a. (2/3)gsinθ
b.(2/3)gcosθ
c gsinθ
d none of these

6 An ice skater spins with arms outstretch at 1.9 rev/s.Her moment of inertia at this time is 1.33 kgm2.She pulls her arms to increase her rate of spin.Her moment of inertia after she pulls her arm is .48kgm2.What is her new rate of spinning
a. 5.26 rev/s
b. 5.2 rev/s
c 4.7 rev/s
d. none of thes

7. MOment of inertia of a uniform rod of lenght L and mass M about an axis passing through L/4 from one end and perpendicular to its lenght
a. 7ML2/36
b.7ML2/48
c. 11ML2/48
d.ML2/12

8. A wheel starts from rest and spins with a constant angular acceleration. As time goes on the
acceleration vector for a point on the rim:

a. increases in magnitude but retains the same angle with the tangent to the rim

b.increases in magnitude and becomes more nearly radial

c. increases in magnitude and becomes more nearly tangent to the rim

d. decreases in magnitude and becomes more nearly radial

9.
Two wheels are identical but wheel B is spinning with twice the angular speed of wheel A. The ratio of the
magnitude of the radical acceleration of a point on the rim of B to the magnitude of the radial acceleration of
a point on the rim of A is:

a. 4
b . 2
c 1/2
d 1/4

10. For a wheel spinning with constant angular acceleration on an axis through its center, the ratio of
the speed of a point on the rim to the speed of a point halfway between the center and the rim is:

a 2
b 1/2
c 4
d 1/4

11. A wheel initially has an angular velocity of 18 rad/s. It has a constant angular acceleration of 2.0 rad/s2 and is
slowing at first. What time elapses before its angular velocity is18 rad/s in the direction opposite to its initial
angular velocity?

a 3 sec
b 6 sec
c 18 sec
d none of these

12. One solid sphere X and another hollow sphere Y are of same mass and same outer radii. Their moment of inertia about their diameters are respectively Ix and Iy such that
(A) Ix= Iy
(B) Ix > Iy
(C) Ix < Iy
(D) Ix/Iy=Dx/Dy
Where Dx and Dy are their densities.

Solutions

1.b
2.b
3.b
4.a
5. a
6 a
7 b
8 b
9 a
10 a
11. c
12 c

### Rotational Short Notes -II

Torque

τ=rXF

Also τ=Iα

Kinetic Energy is pure Rotating body
KE=(1/2)Iω2

Rotational Work Done

-If a force is acting on a rotating object for a tangential displacement of s = rθ (with θ being the angular displacement and r being the radius) and during which the force keeps a tangential direction and a constant magnitude of F, and with aconstant perpendicular distance r (the lever arm) to the axis of rotation, then the work done by the force is:

W=τθ

• W is positive if the torque τ and θ are of the same direction,
otherwise, it can be negative.

Power
P =dW/dt=τω

Angular Momentum

L=rXp
=rX(mv)
=m(rXv)

For a rigid body rotating about a fixed axis
L=Iω

dL/dt=τ

if τ=0 and L is constant

For rigid body having both translation motion and rotational motion

L=L1+L2

L1 is the angular momnetum of Center mass about an stationary axis
L2 is the angular momentum of the rigid body about Center of mass

Law of Conservation On Angular Momentum

If the external torque is zero on the system then Angular momentum remains contants

dL/dt=τext

if τext=0
then dL/dt=0

Equilibrium of a rigid body

Fnet=0 and τext=0

Angular Impulse:

∫τdt term is called angular impluse..It is basically the change in angular momentum

Pure rolling motion of sphere/cylinder/disc

-Relative velocity of the point of contact between the body and platform is zero
-Friction is responsible for pure rolling motion
-Friction is non disipative in nature

E = (1/2)mvcm2+(1/2)Iω2+mgh

### Rotational Short Notes -II

Torque

τ=rXF

Also τ=Iα

Kinetic Energy is pure Rotating body
KE=(1/2)Iω2

Rotational Work Done

-If a force is acting on a rotating object for a tangential displacement of s = rθ (with θ being the angular displacement and r being the radius) and during which the force keeps a tangential direction and a constant magnitude of F, and with aconstant perpendicular distance r (the lever arm) to the axis of rotation, then the work done by the force is:

W=τθ

• W is positive if the torque τ and θ are of the same direction,
otherwise, it can be negative.

Power

P =dW/dt=τω

Angular Momentum

L=rXp
=rX(mv)
=m(rXv)

For a rigid body rotating about a fixed axis
L=Iω

dL/dt=τ

if τ=0 and L is constant

For rigid body having both translation motion and rotational motion

L=L1+L2

L1 is the angular momnetum of Center mass about an stationary axis
L2 is the angular momentum of the rigid body about Center of mass

Law of Conservation On Angular Momentum

If the external torque is zero on the system then Angular momentum remains contants

dL/dtext

if τext=0
then dL/dt=0

Equilibrium of a rigid body

Fnet=0 and τext=0

Angular Impulse:

∫τdt term is called angular impluse..It is basically the change in angular momentum

Pure rolling motion of sphere/cylinder/disc

-Relative velocity of the point of contact between the body and platform is zero
-Friction is responsible for pure rolling motion
-Friction is non disipative in nature

E = (1/2)mvcm2+(1/2)Iω2+mgh

### IIT PHYSICS:Rotational Short notes -I

Angular Displacement

-When a rigid body rotates about a fixed axis, the angular displacement is the angle Δθ swept out by a line passing through any point on the body and intersecting the axis of rotation perpendicularly
-Can be positive (counterclockwise) or negative (clockwise).
-Analogous to a component of the displacement vector.
units: degree, revolution.

Angular Velocity

Average angular velocity, is defined by
\$ = (angular displacement)/(elapsed time) = Δθ/Δt .

Instantanous Angular Velocity ω=dθ/dt

Some points
-Angular velocity can be positive or negative.
-It is a vector quantity and direction is perpendicular to the plane of rotation
-Angular velcity of a particle is diffrent about diffrent points
-Angular velocity of all the particles of a rigid body is same about a point

Angular Acceleration:

Average angular acceleration, is defined by
= (change in angular velocity)/(elapsed time) = Δω/Δt

Instantanous Angular Acceleration
α=dω/dt

Kinematics of rotational Motion
ω=ω0 + αt
θ=ω0t+1/2αt2
ω.ω=ω0.ω0 + 2 α.θ;

Also
α=dω/dt=ωdω/dθ

Vector Nature of Angular Variables
-The direction of an angular variable vector is along the axis.
- positive direction defined by the right hand rule.
- Usually we will stay with a fixed axis and thus can work in the scalar form.
-angular displacement cannot be added like vectors
-angular velocity and acceleration are vectors

Relation Between Linear and angular variables

v=ωXr

Where r is vector joining the location of the particle and point about which angular velocity is being computed

a=αXr

Moment of Inertia

Rotational Inertia (Moment of Inertia) about a Fixed Axis

For a group of particles,

I = mr2

For a continuous body,

I = r2dm

For a body of uniform density

I = ρ∫r2dV

Parallel Axis Therom
Ixx=Icc+ Md2

Where Icc is the moment of inertia about the center of mass

Perpendicular Axis Therom
Ixx+Iyy=Izz

It is valid for plane laminas only

### PMT Test series Index

Mechanics

15 min Test series
PMT test series

### PMT test series for Mechanics

Multiple choice question with one or more answer

1. A body fall from height H.if t1 is time taken for covering first half height and
t2 be time taken for second half.Which of these relation is true for t1 and t2
a. t1 > t2
b. t1 < t2
c t1=t2
d Depends on the mass of the body

2.A 1 kg ball moving at 12 m/s collides head on with 2 kg ball moving with 24 m/s in opposite direction.What are the velocities after collision if e=2/3?
a. v1=-28 m/s,v2=-4 m/s
b. v1=-4 m/s,v2=-28 m/s
c. v1=28 m/s,v2=4 m/s
d. v1=4 m/s,v2=28 m/s

3.A train running at 30m/s is slowed uniformly to a stop in 44 sec.Find the stopping distance?
a. 612 m
b. 662 m
c. 630 m
d. 605 m

4.A nut comes loose from a bolt on the bottom of an elevator as the elavator is moving up the shaft at 3m/s.The nut strikes the bottom of the shaft in 2 sec.How far from the bottom of the shaft was the elevator when nut falls off?
a. 13.6 m
b. 10 m
c. 12.6 m
d. none of these

5.A system consisting of two objects has a total momentum of (18 kgm/sec)i and its center of mass has the velocity of (3 m/s)i.One of the object has the mass 4 kg and velocity (-1.5 m/s)i.The mass and velocity of the other objects are
a. 2 kg, (6 m/s)i
b. 2 kg, (-6 m/s)i
c. 2 kg, (3 m/s)i
d. 2 kg, (-3 m/s)i

6.A moving bullet hits a solid target resting on a frictionless surface and get embeded in it.What is conserved in it?
a. Momentum Alone
b KE alone
c. Both Momentum and KE
d. Neither KE nor momentum

7.A body of mass 5 kg starts from the origin with an intial velocity u=30i+40j m/sec.If the constant force acts on the body F=-(i+5j) N.The time in which y component of the velocity becomes zero is
a. 5 sec
b. 80 sec
c. 20 sec
d. 40 sec

8. A stationary body of mass 3 kg explodes into three equal parts.Two of the pieces fly off at right angles to each other with the velocities 2i m/s and 3j m/s.If the explosion takes place in 10-3 sec.find out the average force action on the third piece in N
a.(-2i-3j)103
b. (2i+3j)103
c (2i-3j)10-3
d. none of these

9.A bullet of mass m is fired horizontally with a velocity u on a wooden block of Mass M suspended from a support and get embeded into it.The KE of th wooden + block system after the collisson
a.m2u2/2(M+m)
b.mu2/2
c. (m+M)u2/2
d. mMu2/2(M+m)

10.A body of Mass M and having momentum p is moving on rough horizontal surface.If it is stopped in distance s.Find the value of coefficient of friction
a.p2/2M2gs
b. p/2Mgs
c. p2/2Mgs
d. p/2M2gs

Solutions
1.a
2.a
3. b
4.a
5 a
6 a
7 d
8 a
9 a
10 a

### IITJEE PHYSICS TESTSERIES:30 Min Objective Test series of Mechanics for IIT/AIEEE/PMT

Multiple choice question with one or more answer

1. A body of mass m is dropped from a certain height.it has velocity v1 when it is at a height h1 above the ground.it has velocity v2 when it is at a height h2 above the ground.which of the following is true
a.v12-v22=2g(h1-h2)
b.v12-v22=2g(h2-h1)
c. v1-v2=√2g(√h2-√h1)
d. v1-v2=√2g(√h1-√h2)

2.A pendulum has a length l.Its bob is pulled aside from its equilibrium position through any angle θ and then released.The speed of the bob when its passes through it equalibrium position
a.√2gl
b. √2gl(1-cosθ)
c.√2glcosθ
d.√2gl(1-sinθ

3.A rockets works on the principle of conservation of
a. Linear momentum
b.mass
c.energy
d. angular momentum

4.A flat car of weight W roll without resistance along on a horizontal track .Intially the car together with weight w is moving to the right with speed v.What invcrement of the velocity car will obtain if man runs with speed reltaive to the floor of the car and jumps of f at the left?
a.wu/w+W
b. Wu/W+w
c. (W+w)u/w
d. none of the above

5.By means of rope ,a body of weight W is moved vertically upward with constant acceleration.Find the tensile force in the rope
a. W(1+a/g)
b W(1-a/g)
c W
d. none of the above

6.The displacement of a particle moving in straight line depends on time t as
x=at3+bt2+ct+d

which of the follwing is true
a. Intial acceleration depends on b only
b Intial velocity depends on c only
c. Intial displacement is d
d. Ratio of intial velocity /intial acceleration depends on a and c

7.A delivery boy wishes to launch a 2.0 kg package up an inclined plane with sufficent speed to reach the top of the incline.The plane is 3 mlong and is inclined at 20.Coefficent of friction between the package and the inclined plane is .40. what minimum intial KE must the boy suply to the package given as sin20=.342 cos20=.940
a 40 J
b. 42.2 J
c. 42.6 J
d. 45 J

8.A given object takes n times as much times to slide down a 45 rough incline as its takes to slide down a perfectly smooth 45 incline.The coefficent f kinectic friction between the objects and incline is gievn by.
a. 1/(1-n2)
b.1-1/n2
c. √1/(1-n2)
d. √(1-1/n2)

9.A uniform chain of length L is lying on the horizontal surface of a table.If the coefficent of friction between the chain and the table top is μ. what is the maximum length of the chain that can hang over the edge of the table without disturbing the rest of the chain on table.?
a.L/(1+μ)
b. μL/(1+μ)
c. L/(1-μ)
d. μL/(1-μ)

10.The coefficent of static and kinectic friction between a body and the surface are .75 and .50 respectively.A force is applied to the body to make it just slide with a constant acceleration which is
a. g/4
b g/2
c. 3g/4
d g

Solutions
1 b
2.b

3. a

4. a

5. a

6. a,b,c

7. b

8. b

9. b

10.a

### 15 Min Objective Test series for Mechanics for IITJEE,AIEEE,PMT

Multiple choice question with one or more answer

1. Which of these is true of a conservative force?
a. Workdone between two points is independent of the path
b. Workdone in a closed loop is zero
c. if the workdone by the conservative is positive,its potential energy increases
d. None of the these

2.A particle is acted upon by a force of costant magnitude which is always perpendicular to the velocity of the particle.The motion of the particle takes place in a plane.it follows that
a. velocity is constant
b. accelerattion is constant
c. KE is constant
d. Particle moves in a circular path

3. A package is dropped out of airplane in a level flight.If air resistance could be neglected.which of these is true
a. Package will follow a parabolic path with respect to a observer on the groud
b Package will follow a vertically straight line path with respect to the observer in the plane.
c.Package will follow a vertically straight line path with respect to a observer on the groud
b Package will follow a parabolic path with respect to the observer in the plane.

4.A small mass m is suspended from one end of a vertical string. and then whirled in a horizontal circle at a constant speed v.
Which of the followings is true
a.The strings stays vertical
b.The string becomes inclined to the vertical.
c.There is no force on mass m except its weight
d.The angle of inclination of the string does not depend on the v
e.The centripetal force on m is mg

5.A IITJEE text book of mass M rests flat on a horizontal table of mass m placed on the ground.Let RX->Y be the constant force exerted by the body x on body Y.Which of the following is true for the forces Rground->table and Rtable->ground
a. It is action and reaction pair
b. have equal magnitude
c. Opposite direction
d.have resultant zero

6.The tension in cable supporting an elevator is equal to th weight of the elevetor.The elevator may be
a. going up with incresing speed
b. going down with increasing speed
c. going up with uniform speed
d. going down with uniform speed.

7 A simple pendulum consists of a mass attached to a light string l. if the system is oscillating through small angles which of the following is true
a.The freqiency is independent of the acceleration due to gravity g
b.The period depends on the amplitude of the ocsillation
c.the period is independent of mass m
d. the period is independent of lenght l

8.A ball is thrown into the air with an intial speed u.The time interval taken for the ball to rise to its maximum height is t1.The time interval taken for the ball to fall back from this maximum height is t2.Under real life condition,which of the following is satisfied
a.t2 > t2
b t2 < t2
c. t2=t2
d. t1 > t2 if u is great enough

9. Let v and a denote the velolcity and acceleratio respectivly of the particle in one dimension motion.
a.the speed of the particle decreases when v.a <0
b. the speed of the particle decreases when v.a >0
c.the speed of the particle increases when v.a=0
d. the speed of the particle decreases when |v|<|a|

10. A refrence frame attached to the earth
a.is an inertial frame by defination
b.cannot be inertial frame as earth is resolving around the sun
c.is an intertial frame because Newton's law are applicable in this frame
d.cannot be intertial frame because earth is rotating about its own axis

Solutions
1.a,b
2.c,d
3.a,b
4. b
5. a,b,c,d
6. c,d
7. c
8 a
9 a
10 b,d

### Challenging Problems in Mechanics to sharpen your mind

1.A particle of mass M is acted upon by a force that has a intial magnitude F0 when t=0 and decrease at a uniform rate until when t=t1,its magnitude is zero.It is moving accross the X-axis.Find the velocity and coordinate of the particle when t=t2 assuming that t2 > t1. Assume xt=0=0 and (dx/dt)t=0=0

Ans
Velcity=F0t1/2M
Displacement=(F0t1/2M)(t2-t1/3)

2.A wheel of radius r rolls without slip along the x-axis. with constant speed. v0.Find out the motion(velocity and acceleration ) of the point A on the rim of the wheel which starts from the origin O.Take Y axis as perpendicular at X axis at origin

Ans

dx/dt=v0[1-cos(v0t/r)]
dy/dt=v0sin(v0t/r)

d2x/dt2=(v02/r)sin(v0t/r)
d2y/dt2=(v02/r)cos(v0t/r)

3.A body moves under the action of a constant force F through fluid that opposes the motion with a force proportional to the square of the velocity that is Ax2.Show that the limiting velocity is VL=(F/A)1/2.

4.A Bungee Jumper is attached to one end of a long elastic rope.The other end of the elastic rope is fixed to a high bridge.The Jumper steps off the bridge and falls from rest towards the river below..he does not hit the river below.The mass of the jumper is M and length of unstretched rope is L.Force constant of the rope is K. and gravitional field strength is g.Mass of rope is negligible ,air resitance is negligible.
1.Find out the distance y dropped by the jumper before coming instantaneously to rest for the first time
2.Maximum speed attained by the jumper during this drop
3.The time taken during the drop before coming to rest for the first time

y=[KL+mg+√(2mgKL+m2g2)]/k
v=√(2gL+mg2/k)
t=√(2L/g) + √(m/k)tan-1{-√(2KL/mg)}

1.Fundamentals of Physics by Resnick Haliday:
It is a nice book having good problems.A good no of checkpoint are there to make you aware of the concept.

2. Feynmann Lectures on Physics:
It is a nice book to prepare for olymiads Physics.The lectures in the book are very good.

3. Irodov Problems in Physics

4. Irodov Solutions I and II

5. Benjamin Crowell Books for Physics

Newtonian Mechanics
Conservation Laws
Vibration and Waves
Electricity and Magnetism

### IITJEE Papers ,Pattern Analysis And old Physics paper

Question Papers

There will be two question papers of three hours duration, each consisting of separate sections in Physics, Chemistry and Mathematics. Questions in these papers will be of objective type, which are to be answered on a specially designed machine-gradable sheet using HB pencils only. Incorrect answers will be awarded negative marks.

Language of Question Papers

Candidates can opt for Question Papers either in English or in Hindi. The option should be exercised while filling the application form. The option cannot be changed at any later stage.

Formats of papers
The two papers had three different parts each, for physics, chemistry and mathematics respectively.
Each part had four sections. They had the following types of questions:

Straight objective type with One answer
These are multiple choice question pattern with one correct option. The questions are elementary and basic concepts are required to solve the question.. find the answer and pick that from among the choices.

Straight objective type with one or more answer
These are multiple choice question pattern with one or more correct option. The questions are elementary and basic concepts are required to solve the question.. find the answer and pick that from among the choices.

Assertion -- reasoning type.
These are bit tough question.This test the real links between the concepts.
Basically Two statements will be there.One statement will be assertion and One will the reason.You will have to tell the link between them ,followings options will be there
a) Statement I is true ,statement II is true ,statement II is correct explanation for statement I
b) Statement I is true ,statement II is true ,statement II is not a correct explanation for statement I
c) Statement I is true,Statement II is false
d) Statement I is False,Statement II is True

You have to chosse the correct one.These questions test the ability to link two diffrent statement.

The three questions that followed a small problem description had to be solved on the basis of the given information. It is basically similar long question asked earliar.Basically they have made it in objective pattern.
The student will need to read the paragraph and apply the knowlegde in the subject to solve the question

Matrix -- match type.
These are column based question.You will need to read the item in column I and related it to the items in Column II.There may be two answer in Column II.

Questions in Physics come from all the modules.But there are some module which are easiar to attempt.

Topics which are scoring and should be cover first in Physics
Thermodynamics
Conduction and Convection of Heat
Hydrostatics and Bernoulli's Principle
Waves in Elastic Media
Interference Beats and Doppler's Effect
Electrostatics (full)
Electromagnetic Induction
Lorentz' Forces
Circuits with Capacitors
Modern Physics (full)
Collisions
Rotational Motion
Gravitation
Elasticity.

IITJEE 2008 Physics analysis
Mechanics
Error analysis:1 Straight objective type with One answer,
Gravitation:1 Straight objective type with One answer,2 Assertion Reason questions
Momentum:1 Straight objective type with One or more answer
Rotational Mechanics: 2 Assertion Reason questions
Fliud Mechanics:1 Assertion Reason questions

Electricty And Magnetism
Magnetic Field:1 Straight objective type with One or more answer
Current Electricity:1 Straight objective type,1 Assertion Reason questions

Modern Physics
X rays:1 Straight objective type.
Binding Energy of Nuclie:2 Straight objective type with One or more answer

Thermodyanamics And Properties of matter
Ideal gas laws:1 Straight objective type.
Properties of matter:1 Linked Comphrehension Type

Optics:1 Straight objective type with One answer,1 Straight objective type with One or more answer

IITJEE solutions for Physics Previous Papers

IITJEE 2008 Physics Part 1
IITJEE 2008 Physics Part 2
IITJEE 2007 Physics Part 1
IITJEE 2007 Physics Part 2
IITJEE 2006 Physics
IITJEE 2005 Physics
IITJEE 2004 Physics
IITJEE 2003 Physics
IITJEE 2002 Physics
IITJEE 2001 Physics

AIEEE solutions for Physics Previous paper

AIEEE 2008 Physics
AIEEE 2007 Physics
AIEEE 2006 Physics
AIEEE 2005 Physics
AIEEE 2004 Physics
AIEEE 2003 Physics

### Problem Solving tips for IITJEE Mechanics

Vector Mathematics

You will come across vectors in physics problem very frequently.So it is must to know to solve the vector mathematics in short time.And Making sure you have done in correctly.You will find vectors in every module be it mechanics ,electrostatics,magentics

When you need to add or substract two or more vectors, you can use following procedure

1. Select a coordinate system that is convenient. (Try to reduce the number of
components you need to find by choosing axes that line up with as many
vectors as possible.)

2. Draw a labeled sketch of the vectors described in the problem.

3. Find the x and y components of all vectors

4. Compute the resultants in x and y direction

5. If necessary, use the Pythagorean theorem to find the magnitude of the resultant vector and select a suitable trigonometric function to find the angle
that the resultant vector makes with the x axis.

Products
When u need to perform scalar or vector product.It is nice to following procedure

1. Select a coordinate system(x,y,z) that is convenient. (Try to reduce the number of
components you need to find by choosing axes that line up with as many
vectors as possible.).Use i,j,k as the unit vector across x,y,z axis.

2. Draw a labeled sketch of the vectors described in the problem.

3. Express all the vector in form in i,j,k forms

4. Perform the multipication

Motion in a Two dimensional Plane

- Select a coordinate system and resolve the initial velocity vector into x and y
components.

-Find out acceleration in each direction and solve in each direction according to one rectilinear motion equation.

-if the acceleration is in vertical direction only.Follow the techniques for solving constant-velocity problems to analyze the horizontal motion. Follow the techniques for solving constant-acceleration problems to analyze the vertical motion. The x and y motions share the same time of flight t.

- There might be question about trajortory in the Problem ,find out the motion in x and y direction with respect to time from previous point.And then find the value of t from one equation and then put that value in another equation to find out the equation of trajactory

Motion in a Three dimensional Plane

- Select a coordinate system and resolve the initial velocity vector into x , y and z components

-Find out acceleration in each direction and solve in each direction according to one rectilinear motion equation.

Uniform Circular Motion

-Draw a simple, neat diagram of the system.

-Firstly consider the origin of the forces acting on the each object.To do this find out the field forces acting on the each object.Wherever contact in available account the contact force carefully

-Find out the force acting on the body.The resultant force should provide the required centrepatal required for Circular motion

-Centrepatal force=mv2/R will give the velotiy accordingly.

Newtons Law Problem
-Draw a neat diagram of the system.

-Firstly consider the origin of the forces acting on the each object.To do this find out the field forces acting on the each object.Wherever contact in available account the contact force carefully

-Isolate the body whose motion is to be analyzed. Draw a free-body diagram for this body. For systems containing more than one objects, draw separate free-body diagrams for each objects This way there will not any confusion about the force acting on each object.Newtons Third law will help in obtaining the action reaction pair. Do not include in the free-body diagram forces exerted by the object on its surroundings. Establish convenient coordinate axes for each objects and find the components of the forces along these axes.

- Use pseudo force if viewing from the non intertial frame of refrence

-Apply Newton's second law, F= ma, in component form.

-Solve the component equations for the unknowns. Remember that you must have as many independent equations as you have unknowns to obtain acomplete solution.

-Make sure your results are consistent with the free-body diagram.

- If the object are attached to each others by the strings,then make use of constraints theory to find out the acceleration equation between the objects

Work And Energy

- Choose your frame of refrence.KE will differ in each refrence frame while PE will remains constant

-Define your system, which may include two or more interacting particles, as well as springs or other systems in which elastic potential energy can bestored. Choose the initial and final points.

-Identify zero points for potential energy (both gravitational and spring). If there is more than one conservative force, write an expression for the potential energy associated with each force.

-Determine whether any nonconservative forces are present. Remember that if friction or air resistance is present, mechanical energy is not conserved.

-Determine whether any external forces are present. Remember that external forces are present, mechanical energy is not conserved.

-If mechanical energy is conserved, you can write the total initial energy at some point Ei=PEi+KEi. Then, write an expression for the total final energy at the final point that is of interest Ef=PEf+KEf. Because mechanical
energy is conserved, you can equate the two total energies and solve for the quantity that is unknown.

-If frictional forces are present (and thus mechanical energy is not conserved), first write expressions for the total initial and total final energies. In this case, the difference between the total final mechanical energy and the total initial mechanical energy equals the change in mechanical energy in the system
due to friction.

-If external forces are present (and thus mechanical energy is not conserved), first write expressions for the total initial and total final energies. In this case, the difference between the total final mechanical energy and the total initial mechanical energy equals the change in mechanical energy in the system
due to external force.

-If both external forces and frictional forces are present (and thus mechanical energy is not conserved), first write expressions for the total initial and total final energies. In this case, the difference between the total final mechanical energy and the total initial mechanical energy equals the change in mechanical energy in the system due to external force and friction

Momentum and Collisions

- Choose your frame of refrence

-Set up a coordinate system and define your velocities with respect to that system.It is usually convenient to have the x axis coincide with one of the initial velocities.

-In your sketch of the coordinate system, draw and label all velocity vectors and include all the given information.

-Write expressions for the x and y components of the momentum of each object before and after the collision. Remember to include the appropriate signs for the components of the velocity vectors.

-Write expressions for the total momentum in the x direction before and after
the collision and equate the two. Repeat this procedure for the total momentum
in the y direction. These steps follow from the fact that, because the momentum of the system is conserved in any collision(law on conservation of linear momentum), the total momentum along any direction must also be constant. Remember, it is the momentum of the system that is constant, not the momentan of the individual objects.

-If the collision is inelastic, kinetic energy is not conserved, and additional information is probably required. If the collision is perfectly inelastic, the final velocities of the two objects are equal. Solve the momentum equations for the unknown quantities.

-If the collision is elastic, kinetic energy is conserved, and you can equate the
total kinetic energy before the collision to the total kinetic energy after the
collision to get an additional relationship between the velocities.And you can solve the energy and momentum equation to find out the find velocities.

- Centre of mass can be useful feature in solving the momentum problems

Body in Static equilibrium

-Draw a neat diagram of the system.

-Firstly consider the origin of the forces acting on the each object.To do this find out the field forces acting on the each object.Wherever contact in available account the contact force carefully

-Isolate the object being analyzed. Draw a free-body diagram and then show
and label all external forces acting on the object, indicating where those forces are applied.This way there will not any confusion about the force acting on each object.Newtons Third law will help in obtaining the action reaction pair. Do not include forces exerted by the object on its surroundings.(For systems that contain more than one object, draw a separate free-body diagram for each one.) Try to guess the correct direction for each force. If the direction you select leads to a negative force, do not be alarmed; this merely means that the direction of the force is the opposite of what you guessed.

-Establish a convenient coordinate system for the object and find the components of the forces along the two axes. Then apply the first condition for equilibrium. Remember to keep track of the signs of all force components.

-Choose a convenient axis for calculating the net torque on the object. Remember that the choice of origin for the torque equation is arbitrary; therefore, choose an origin that simplifies your calculation as much as possible.
Note that a force that acts along a line passing through the point chosen as
the origin gives zero contribution to the torque and thus can be ignored.

### Thermodynamics Numerical

1.An ideal diatomic gas is enclosed in an insulated chamber at temperature 300K. The chamber is closed by a freely movable massless piston, whose initial height from the base is 1m. Now thegas is heated such that its temperature becomes 400 K at constant pressure. Find the new height of the piston from the base.If the gas is compressed to initial position such that no exchangeof heat takes place, find the final temperature of the gas.

2.A cylinder of mass 1 kg is given heat of 20000J at atmospheric pressure. If initially temperature of
cylinder is 200C, find
(a) final temperature of the cylinder.
(b) work done by the cylinder.
(c) change in internal energy of the cylinder.
(Given that Specific heat of cylinder= 400 J kg-1 0C–1, Coefficient of volume expansion
= 9 × 10-5 °C-1, Atmospheric pressure = 105 N/m2 and Density of cylinder = 9000 kg/m3)

3.A gas container has a walls that can bear maximum pressure of 2.2*106 pa.The container contains gas at 4*105 pa and 350K.If the container is steadly heated then neglecting change in volume .Calculate the temperarture at which container will break?

4.A vessel of volume V=20L contains a mixture of hydrogen and helium at T=20° C and Pressue P=2.0 atm.The mass of the mixture is equal to m=5g.Find the ratio of the mass of the hydrgen to that mass of the helium in the mixture Given R=.082 L.atm.mol-1.K-1

5.The first law of thermodynamics dU=dQ-dW,indicates that when a system goes from its intial state to a final state
a. dU is same for every path
b. dQ is same for evry path
c dQ+dW is same for every path
d dQ-2dW is same for every path

### Physics Champion Contest-2

Welcome to the Physics Champion Contest!!!!!!!!!!!

We present the First Physics Champion Contest

Physics Champion Contest-2

Winner will get stationary gift pack worth Rs 200.!!!!!!!!!!!!!!!!!!!!!

Procedure
1 This contest is for all the students studying in 10th to 12th ,students preparing Engineering and Medical examination
2.There are 5 multiple choice questions.You have pick the correct choice ,send to us in Format given below
3.You will be choosen for lucky draw only when all the question are correct.
4. Winner will be choosen from the lucky draw from All those candidate who give all write answer
5. In the format given below,you have to also write the name of the friends who reffred you this site
There is lot of importance of this field.Let me explain that
Based on the data provided by you all,we will make a list like this

Candidate:No of times it is refrered

If that candidate has sent the entry for the contest and also if he qualifies for the lucky draw,then his name will be

entered in the lucky draw as many times as he was refrred.
So students you good chance of winning,if you reffred this site to more and more people

6 You have to send the answer and the information to the following mail address in following format

Subject:Physics Champion Contest-I

Body:

Name:
Father's Name:
Refrred by:

1.
2.
3.
4.
5.

Thanks

7 This contest is valid from 23 July 2008 to 15 June 2008.Winner will be announced on the site on 30 Sep 2008.
8.I will cover the cost of shipping. There is no cost to you.

Contest Questions

Multiple choice question with one or more answer

1. A block of mass M is pulled along a horizontal friction surface by a rope of mass m. If a force P is applied at the free end of the rope, the force exerted by the rope on the block is
a)Pm/m+M
b)P
c)PM/m+M
d)Pm/M-m

2.A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift moves downward with an acceleration of 5 m/s2, the reading of the spring balance will be
(A) 24 N
(B) 74 N
(C) 15 N
(D) 49 N

3. Which of the following functions represent a travelling wave
a. y=pcos(qx)sin(rt)
b. y=psin(qx+rt)
c. y=psin(qx-rt)
d. none of the above

4.There are two statement about Ideal gases
A. The Vrms of gas molecules depends on the mass of the gas molecule and the temperature
B. The Vrms is same for all the gases at the same temperature
which one of the following is correct
a. A and B both
b. A only
c B only
d. A and B both are incorrect

5. A particle moves in a straight line according to
x=t3-4t2+3t

Find the acceleration of the particle at displacement equal to zero
a.(-8,-2,10)
b. (-1,-2,10)
c. (8,2,10)
d. (1,2,10)

### Thermodynamics IITJEE test series -2

Mulitiple Choice questions with Single answer

1. Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature T0, while Box B contains one mole of helium at temperature (7/3) T0.The boxes are then put into thermal contact with each other and heat flows between them until
the gases reach a common final temperature. (Ignore the heat capacity of boxes). Then, the finaltemperature of the gases, T, in terms of T0 is
a)T=5/2T0
b.T=3/7T0
c.T=7/3T0
d.T=3/2T0

2.According to Newton’s law of cooling, the rate of cooling of a body is proportional to (T)n, where T is the difference of the temperature of the body and the surroundings, and n is equal to
(A) two
(B) three
(C) four
(D) one

3.The pressure of the gas in constant volume gas thermometer are 80 cm,90cm and 100cm of mercury at the ice point,the steam point and in a heated wax bath resp.Find the temperature of the wax bath
a)200° C
b)201° C
c)202° C
d) none of the above

4.The pressure P of one mole of gas varies with volume V as
P=4-3V2
Highest absolute temperature to gas can be heated is
a.16/9R
b.9/16R
c 1/16R
d None of the above

5.A sphere,a cube and a circular plate have the same mass and are made of same material.All of them are at the same temperatrure T.Which one will have maximum rate of cooling.
a. Sphere
b Cube
c. Circular plate
d. All will have same rate of cooling

Mulitiple Choice questions with More than one answer

6.For an ideal gas
a) Heat added or Heat taken is not null in adiabatic process
b) Internal energy does not change in the isothermal process
c) Change is internal energy is zero in the cyclic process
d. None of the above

7).In which of the following process,convection does takes place
a. sea and land breeze
b.boiling of the water
c.heating air around the furnace
d.warming of glass of bulb due to filament

8)if a gas has n degrees of freedom.Then the expression (Cp/Cp) +1 is equal to
a) 2(1/n +1)
b) 2(n + 1/2)
c) 2+n/2
d) none of the above

Assertion and Reason
a) Statement I is true ,statement II is true ,statement II is correct explanation for statement I
b) Statement I is true ,statement II is true ,statement II is not a correct explanation for statement I
c) Statement I is true,Statement II is false
d) Statement I is False,Statement II is True

9. STATEMENT 1:The molar specfic heat capacity of the ideal gas in isothermal process is infinity
STATEMENT 2:Heat transfer is non zero in the Isothermal process

10.STATEMENT 1:Equation of state for a real gas is (P+a/V2)(V-b)=nRT

STATEMENT 2: Molecular attraction is not neglible and the size of molecules are not neglibile in comparison to average sepeartion between them

11.STATEMENT 1:Root mean square velocity of the gas does not change in a Isothermal process
STATEMENT 2:Isothermal process may be achieved by immersing the system in large reservior and performing the process slowly

Matrix Match type
12 Three identical cylinder A1,A2,A3 contains equal moles of Helium,Nitrogen,Carbon dioxide at the same temperature

Match the column I to column II

A)Traslational Energy is maximun in the cylinder
B)Total energy is minimum in the cylinder
C)Root mean square velocity is maximum in the cylinder
D)Mean speed will be minimum in the cylinder

P) A1
Q) A2
R) A3
S) No appropiate match given

A box Of interior Volumme V1 has a heavy airtight hinged lid of mass M and area A.The box contains n1 moles of gas at Temperature T0.The box is inside a chamber which also contains additional n2 moles of the same gas at the same temperature..The gas in the chamber occupies the volume V2.

13 find the pressure of the gas in the box
a)n1RT0/V1
b)n2RT0/V2
c)(n1+n2)RT/(V1+V2)
d) none of the above.

14 find the pressure of the gas in the chamber
a)n1RT0/V1
b)n2RT0/V2
c)(n1+n2)RT/(V1+V2)
d) none of the above.

15.Intailliy the hinged lid is closed.Then which of these expression is true
a.(n1RT0/V1) -(n2RT0/V2) <=Mg/A
b. (n1RT0/V1) -(n2RT0/V2) => Mg/A
c. (n2RT0/V2) -(n1RT0/V1) => Mg/A
d. (n2RT0/V2) -(n1RT0/V1) <= Mg/A

16.If the whole system is heated,at what temperature T will the gas pressure lift the hinged lid
a)T=Mg/RA(n1/V1 -n2/V2)
b)T=Mg/RA(n2/V2 -n1/V1)
c)T=Mg/RA(n1/V1 +n2/V2)
d) None of the above

### Physics Champion Contest -1 Winner

Hi All

We receive lot of entries for the contest.Thanks all for the Response

1.A
2. A
3.A and C
4. A,B,C
5.B

The winner of the contest is Muni Agarwal from Nainital
He will soon recive the stationary Gift worth RS 200

Thanks to all overwhelming response!!!!!

### Mechanics Test Series -II

Multiple choice question with one or more answer
1. A block of mAss M is moving with a velocity v on straight surface.What is the shortest distance and shortest time in which the block can be stopped if μ is coefficent of friction
a.v2/2μg,v/μg
b. v2/μg,v/μg
c.v2/2Mg,v/μg
d none of the above

2.A horizontal force of F N is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is μ. The weight of the block is
a.μF
b. F(1+μ)
c. F/μ
d none of these

3.Consider the following two statements.
STATEMENT 1 Linear momentum of a system of particles is zero.
STATEMENT 2 Kinetic energy of system of particles is zero.
(A) A does not imply B and B does not imply A.
(B) A implies B but B does not imply A
(C) A does not imply B but b implies A’
(D) A implies B and B implies A.

4.The Position vector of the center of mass of uniform semi circular ring of radius R and Mass M whose center coincided with the origin
a.r=(2R/π)j
b.r=(R/π)j
c.r=(4R/π)j
d. none of the these

5.A body is sliding down a rough inclined plane of angle of inclination θ for which coefficent of friction varies with distance y as μ(y)=Ky where K is constant.Here y is the distance moved by the body down the plane.The net force on the body is zero at A.Find the value of constant K
a. tanθ/A
b. Acotθ
c. cotθ/A
d. A tanθ

6.Chosse the correct option
a.if Workdone by the conservative force is positive then Potential energy decreases
b. Rate of change of momentum of many particles system is proportional to net external force on the system
c.The workdone by the conservative force in closed loop is zero
d. None of the above

7.Two electrons(e) are the at the point (-a,0) and (a,0).Their mass is m.They are released from rest.The acceleration of the center of mass of the system when the electron at 4a distance apart
a. e2/64mπε0a2
b. zero
c. e2/16mπε0a2
d. none of the above

8.The potential energy of a certain particle is given by
U=20x2+35z3.Find the vector force on it
a. -40xi-105z2k
b. 40xi-105z2k
c.-10xi-105z2k
d 40xi+105z2k

Matrix Match type

9.
Column I
a. Frictional force
b. Gravitational force
c. Electrical force
d Viscous force

Column II
P. Workdone by the force in closed loop is zero
Q. Workdone by the force in closed loop is not zero

### Mechanics Test Series -II

Multiple choice question with one or more answer
1. A block of mAss M is moving with a velocity v on straight surface.What is the shortest distance and shortest time in which the block can be stopped if μ is coefficent of friction
a.v2/2μg,v/μg
b. v2/μg,v/μg
c.v2/2Mg,v/μg
d none of the above

2.A horizontal force of F N is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is μ. The weight of the block is
a.μF
b. F(1+μ)
c. F/μ
d none of these

3.Consider the following two statements.
STATEMENT 1 Linear momentum of a system of particles is zero.
STATEMENT 2 Kinetic energy of system of particles is zero.
(A) A does not imply B and B does not imply A.
(B) A implies B but B does not imply A
(C) A does not imply B but b implies A’
(D) A implies B and B implies A.

4.The Position vector of the center of mass of uniform semi circular ring of radius R and Mass M whose center coincided with the origin
a.r=(2R/π)j
b.r=(R/π)j
c.r=(4R/π)j
d. none of the these

5.A body is sliding down a rough inclined plane of angle of inclination θ for which coefficent of friction varies with distance y as μ(y)=Ky where K is constant.Here y is the distance moved by the body down the plane.The net force on the body is zero at A.Find the value of constant K
a. tanθ/A
b. Acotθ
c. cottanθ/A
d. Atantanθ

6.Chosse the correct option
a.if Workdone by the conservative force is positive then Potential energy decreases
b. Rate of change of momentum of many particles system is proportional to net external force on the system
c.The workdone by the conservative force in closed loop is zero
d. None of the above

7.Two electrons(e) are the at the point (-a,0) and (a,0).Their mass is m.They are released from rest.The acceleration of the center of mass of the system when the electron at 4a distance apart
a. e2/64mπε0a2
b. zero
c. e2/16mπε0a2
d. none of the above

8.The potential energy of a certain particle is given by
U=20x2+35z3.Find the vector force on it
a. -40xi-105z2k
b. 40xi-105z2k
c.-10xi-105z2k
d 40xi+105z2k

Matrix Match type

9.
Column I
a. Frictional force
b. Gravitational force
c. Electrical force
d Viscous force

Column II
P. Workdone by the force in closed loop is zero
Q. Workdone by the force in closed loop is not zero