A block of mass m is projected with speed v along the rough surface of an inclined plane of height h. If block comes to rest at the top of the surface, then work done by friction force is

1.  $-\frac{1}{2}{\mathrm{mv}}^2$

2.  $\mathrm{m}\left[\mathrm{gh} - \frac{1}{2}{\mathrm{v}}^2\right]$

3.  -mgh

4.  $\mathrm{m}\left[\mathrm{gh} + \frac{1}{2}{\mathrm{v}}^2\right]$

If a body starts its motion along the smooth track from P as shown in the figure, then its velocity at the instant of leaving R is

(1)  5 m/s 

(2)  15 m/s

(3)  10 m/s

(4)  20 m/s

The principle of conservation of energy and conservation of mechanical energy applicable respectively for

(1)  Conservative and non-conservative forces

(2)  Conservative and conservative force

(3)  Non-conservative and conservative forces

(4)  All forces and conservative forces

A particle of mass m is moving in a vertical circle of radius r. If the velocity of the particle at the uppermost point is $\sqrt{2gr}$, then its velocity at the lowermost point

(1)  $\sqrt{7\mathrm{gr}}$

(2)  $\sqrt{6gr}$

(3)  $\sqrt{5gr}$

(4)  2$\sqrt{gr}$

A person applies a force \(\vec F\) on a box inside a moving train. If \(S_1\) is the displacement of box with respect to train and \(S_2\) is the displacement of train with respect to ground, then the work done by the person in the frame of the earth will be:
1. \(\vec F \cdot \vec{S_1}\)
2. \(\vec F \cdot \vec{S_2}\)
3. \(\vec F \cdot (\vec{S_1}+ \vec{S_2})\)
4. \(\vec F \cdot (\vec{S_1}- \vec{S_2})\)

A block having mass m is hanging by a string of length l. A variable horizontal force is applied on the block, which displaces the block slowly till the string makes an angle $\mathrm{\theta }$ with the vertical. Find the work done by the force.

(1)  mgl

(2)  mgl(1 - cos$\mathrm{\theta }$)

(3)  mglcos$\mathrm{\theta }$

(4)  mgl(1 + cos$\mathrm{\theta }$)

A particle is moving with kinetic energy E and momentum p. Which of the following graphs is possible between $\sqrt{E}$ and $\frac{1}{p}$?

1.  

2.  

3.  

4.  

Two vehicles are moving with the same kinetic energy. If the ratio of their masses is 1 : 3 then find the ratio of their stopping distances when both vehicles stop with the same retardation.

(1)  1: 1

(2)  3: 1

(3)  9: 1

(4)  1: 9

If the work done by the string on block A is W. Then work done by the string on the block B will be

(1)  -W

(2)  $-\frac{\mathrm{W}}{2}$

(3)  2W

(4)  Zero