## A ball is projected with initial velocity u at Angle Ɵ with horizontal Then, horizontal displacement covered by the ball as it collides third time with the ground would be

Q: A ball is projected with initial velocity u at Angle Ɵ with horizontal Then, horizontal displacement covered by the ball as it collides third time with the ground would be (coefficient of restitution is e)

(a) $\displaystyle (1 + e) \frac{u^2 sin⁡2\theta}{g}$

(b) $\displaystyle (1 + e + e^2 ) \frac{u^2 sin⁡2\theta}{2 g}$

(c) $\displaystyle e \frac{u^2 sin⁡2\theta}{g}$

(d) $\displaystyle (1 + e + e^2) \frac{u^2 sin⁡2\theta}{g}$

Ans: (d)

## A sphere moving with velocity v strikes elastically with a wall moving towards the sphere with velocity u. If the mass of the wall is infinitely large, the work done by the wall during collision will be

Q: A sphere moving with velocity v strikes elastically with a wall moving towards the sphere with velocity u. If the mass of the wall is infinitely large, the work done by the wall during collision will be

(a) mu (u + v)

(b) 2 mu(u + v)

(c) (2/3) mu(u + v)

(d) (3/2) mu (u + v)

Ans: (b)

## The bob of a pendulum of length 980 cm is released from rest with its string making an angle 600 with the vertical. It collides with a ball of mass 20 g resting on a smooth horizontal surface at the position of rest of pendulum. If the collision? Mass of the bob is 10 g.

Q: The bob of a pendulum of length 980 cm is released from rest with its string making an angle 600 with the vertical. It collides with a ball of mass 20 g resting on a smooth horizontal surface at the position of rest of pendulum. If the collision? Mass of the bob is 10 g.

(a) 490 cm/s

(b) (2/3) × 980 cm/s

(c) 980/4 cm/s

(d) 980/3 cm/s

Ans: (d)

## A piece of wood of mass 0.03 kg is dropped from the top of a building 100 m high. At the same time, a bullet of mass 0.02 kg is fired vertically upward ….

Q : A piece of wood of mass 0.03 kg is dropped from the top of a building 100 m high. At the same time, a bullet of mass 0.02 kg is fired vertically upward with a velocity of 100 ms-1 from the ground, The bullet gets embedded in the wooden piece after striking. Find the height to which the combination rises above the building before it starts falling.

(a) 46.5 m

(b) 41.6 m

(c) 49.7 m

(d) 52.3 m

Ans: (b)

## A sphere of mass m, impinges obliquely on a sphere of mass M which is at rest. The directions of motion of the sphere make an angle x with each other after impact. If m = e M

Q: A sphere of mass m, impinges obliquely on a sphere of mass M which is at rest. The directions of motion of the sphere make an angle x with each other after impact. If m = e M (where, e is coefficient of restitution), then x is

(a) π/3

(b) π/2

(c) π/6

(d) π/4

Ans: (b)