A body of \(10\) kg is subjected to a force as shown in the figure. The block moves along a straight line under the influence of this force. The change in kinetic energy when the body moves from \(x=0\) to \(x=4\) m will be:

               

1. \(15\) J
2. \(12.5\) J
3. \(17.5\) J
4. \(19.2\) J

A constant horizontal force is applied on a block kept at rest on a smooth horizontal surface. Its power \((P)\) versus time \((t)\) graph is best shown by:

1.		2.
3.		4.

A block slides down an inclined plane of inclination \(30^{\circ}\) with a constant velocity. It then projected up with an initial speed of \(6~\text{m/s}\), the distance moved by it on the inclined before coming to rest is:
1. \(1.5~\text{m}\)
2. \(1.8~\text{m}\)
3. \(2.0~\text{m}\)
4. \(2.4~\text{m}\)

The potential energy of a particle of mass 0.5 kg moving along x axis is given by

U = 2x (x - 3). The speed of the particle is maximum at

(1)  x = 1 m

(2)  x = 1.5 m

(3)  X = 2 m

(4)  x = 3 m

Work energy theorem is valid in

(1)  Only inertial frame of reference

(2)  The only non-inertial frame of reference

(3)  Both inertial and non-inertial frame of reference

(4)  Does not depend on any frame of reference

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$\sqrt{gr}$