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)

1.	Potential energy will be maximum at \(0.5~\text{s}.\)
2.	Kinetic energy will be maximum again at \(1~\text{s}.\)
3.	Kinetic energy = potential energy at a height of \(2.5~\text{m}\) from the ground.
4.	Potential energy will be minimum at \(1~\text{s}.\)

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

A ball is dropped from a height h on a stationary floor and rebounds. If the coefficient of restitution is 0.5, then the total distance covered by the ball before it strikes the floor for 3rd time is:

1.  2h

2.  $\frac{13\mathrm{h}}{8}$

3.  $\frac{3\mathrm{h}}{2}$

4.  $\frac{4\mathrm{h}}{3}$

A particle is projected at a time \(t=0\) with a speed \(v_{0}\)${\mathrm{}}_{}$ and at an angle with the horizontal in a uniform gravitational field. Then which of the following graphs represents power delivered by the gravitational force against time \((t)?\)

1.		2.
3.		4.

Two balls having different masses are moving towards each other with speed 30 m/s and 20 m/s as shown in figure (i). Their velocities after collision become 20 m/s and 30 m/s as shown in the figure (ii), then the coefficient of restitution is:

(1)  1

(2)  0.5

(3)  0.4

(4)  0.2