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

If the pulley system with the ideal mechanical advantage of 4 requires a force of 15 N to lift a load of 45 N, then the efficiency of the pulley is

(1)  25%

(2)  30%

(3)  40%

(4)  75%

A small block of mass \(m\) is pulled by a light rope on a quarter circular track, having radius \(R\). If the force applied on the rope is \(F\) always directed horizontally, then the work done by the force till the block reaches from \(A\) to \(B\) is:

1. \(FR\)
2. \(FR\sqrt{2}\)
3. \(2\pi F R\)
4. zero

A stone of mass m is thrown from the earth's surface at an angle $\mathrm{\alpha }$ to the horizontal with an initial velocity ${\mathrm{v}}_0$. Ignoring the air drag, the power developed by gravitational force t second after the beginning of motion is:

(1)  $\mathrm{mg}\left(\mathrm{gt} - {\mathrm{v}}_0\mathrm{sin\alpha }\right)$

(2)  ${\mathrm{mgv}}_0\mathrm{sin\alpha }·\mathrm{t}$

(3)  $\mathrm{mg}\left(\mathrm{g} - \mathrm{vsin\alpha }·\mathrm{t}\right)$

(4)  Zero

A car of mass 100 kg and traveling at 20 m/s collides with a truck weighing 1 tonne traveling at 9 km/h in the same direction. The car bounces back at a speed of 5 m/s. The speed of the truck after the impact will be:

1.  11.5 m/s

2.  5 m/s

3.  18 m/s

4.  12 m/s