mechanics test questions

Question 1
A ball is thrown vertically upwards with a velocity u from top of a tower. It strikes the ground with a velocity 3u. The time taken by the ball to reach the ground is given by
(a) u/g
(b) 2u/g
(c) 3u/g
(d) 4u/g

Question 2
A body slides down an inclined plane of inclination . The coefficient of friction down the plane varies in the direct proportion to the distance moved down the plane(=kx). The body will move down the plane with
(a) constant acceleration =gsin
(b) constant acceleration =(gsin-gcos)
(c) constant retardation =(gcos-gsin)
(d) variable acceleration that first decreases from gsin to zero and that becomes negative.

Question 3
A escalator is moving downwards with a uniform speed u. A man of mass m is running upwards on it at a uniform speed v. If the height of escalator is h, the work done by man in going up the escalator is
(a) zero
(b) mgh
(c) mghu/(v-u)
(d) mghv/(v-u)

Question 4
A particle moves in a circular orbit with a uniform angular speed. However , the plane of the circular orbit is itself rotating at a constant angular speed. We may then say that
(a) the angular velocity as well as angular acceleration of particle are both constant.
(b) neither the angular velocity nor the angular acceleration of the particle are constant.
(c) the angular velocity of the particle varies but its angular acceleration is constant.
(d) the angular velocity of the particle remains constant but the angular acceleration varies.
Question 5
Two objects of mass m and 4m are at rest at infinite separation. They move towards each other under mutual gravitational attraction. Then at separation r, which one of the following is true.
(a) the total energy of the system is not zero
(b) the force between them is not zero
(c) the center of mass of the system is at rest
(d) all the above are true

1. b
2. d
3. d
4. c
5. d

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