Which of the following remains unchanged (for the system) during an inelastic collision?

1.	Mechanical energy	2.	Kinetic energy
3.	Momentum	4.	All of the above.

The position (in meter) of a particle of mass 1 kg confined to move along the y-axis varies with time (in second) as y= ${\mathrm{t}}^2$ - 4t+ 5. The work done by all the forces acting on the particle during t = 0 to t = 4 s is

(1)  8 J

(2)  16 J

(3)  32 J

(4)  Zero

A particle is dropped from a height of 50 m. If the particle loses its 20% mechanical energy during the impact with the ground, up to what height will it rebound after the second impact?

(1)  40 m

(2)  36 m

(3)  32 m

(4)  28 m

A body of mass 2 kg is rotating in a vertical circle of radius 4 m. The difference in its kinetic energy at the top and bottom of the circle is:

(1)  40 J

(2)  80 J

(3)  120

(4)  160 J

If a stone is projected vertically upward from the ground with a speed of \(10~\text{m/s}\), then its:
(take \(g=10\) m/s²)

A body of mass m strikes with the ground with speed u and coefficient of restitution is e, then find the work done by normal reaction force on the body.

1.  zero

2.  $\frac{1}{2}{\mathrm{mu}}^2\left({\mathrm{e}}^2 - 1\right)$

3.  $\frac{1}{2}{\mathrm{mu}}^2\left(1 - {\mathrm{e}}^2\right)$

4.  $\frac{1}{2}{\mathrm{mu}}^2$

A particle suspended by a light inextensible thread of length l is projected horizontally from its lowest position with velocity $\sqrt{4gl}$. The height from its lowest position at which particle will leave the circular path is:

1.  $\frac{3\mathrm{l}}{2}$

2.  $\frac{5l}{3}$

3.  $\frac{4l}{3}$

4.  2l

A mass M is suspended by a spring having a spring constant K. In equilibrium position mass M is given a speed u. Find further extension in the spring.

1.  $\sqrt{\frac{\mathrm{M}}{\mathrm{K}}}\mathrm{u}$

2.  $\sqrt{\frac{2\mathrm{M}}{\mathrm{K}}}\mathrm{u}$

3.  $\sqrt{\frac{\mathrm{M}}{\mathrm{K}}}\mathrm{u} + \frac{\mathrm{Mg}}{\mathrm{K}}$

3.  $\sqrt{\frac{2\mathrm{M}}{\mathrm{K}}}\mathrm{u} + \frac{\mathrm{Mg}}{\mathrm{K}}$

A ball 'P strikes elastically with another identical ball Q resting on a smooth surface with velocity v. The ratio of the speeds of ${\mathrm{v}}_{\mathrm{P}} : {\mathrm{v}}_{\mathrm{e}}$ two balls after the collision is

(1)  1: $\sqrt{3}$

(2)  $\sqrt{3}$:1

(3)  1:2

(4)  $\sqrt{3}$:2

A block of mass 20 kg is being brought down by a chain. If block acquires a speed of 2 m/s in dropping down 2 m. Find work done by the chain during the process. (g = 10 $\mathrm{m}/{\mathrm{s}}^2$)

(1)  -360 J

(2)  400 J

(3)  360 J

(4)  -280 J