## Pages

### 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