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 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 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 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.

The potential energy \(\mathrm{U}\) of a system is given by $\mathrm{U}=$ $\mathrm{A}$ $-$ ${\mathrm{Bx}}^2$ (where \(\mathrm{x}\) is the position of its particle and \(\mathrm{A},\) \(\mathrm{B}\) are constants). The magnitude of the force acting on the particle is:
1. constant

2. proportional to \(\mathrm{x}\)

3. proportional to ${\mathrm{x}}^2$

4. proportional to $\left(\frac{1}{\mathrm{x}}\right)$

A person-1 stands on an elevator moving with an initial velocity of 'v' & upward acceleration 'a'. Another person-2 of the same mass m as person-1 is standing on the same elevator. The work done by the lift on the person-1 as observed by person-2 in time 't' is:

1.  $\mathrm{m}\left(\mathrm{g}\right)$ $+$ $\mathrm{a}\left(\mathrm{vt}\right)$ $+$ $\frac{1}{2}{\mathrm{at}}^2$

2.  $-\mathrm{mg}\left(\mathrm{vt}\right)$ $+$ $\frac{1}{2}{\mathrm{at}}^2$

3.  0

4.  $\mathrm{ma}\left(\mathrm{vt}\right)$ $+$ $\frac{1}{2}{\mathrm{at}}^2$