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

If work done by the string on block A is W, shown in the given arrangement, then the work done by the string on block B is

1.  -W

2.  $-\frac{2\mathrm{W}}{3}$

3.  $\frac{3\mathrm{W}}{2}$

4.  $\frac{2\mathrm{W}}{3}$

Which of the following remains unchanged (for the system) during an inelastic collision?

The position (in meter) of a particle of mass 1 kg confined to move along the y-axis varies with time (in second) as y= ${\mathrm{t}}^2$ - 4t+ 5. The work done by all the forces acting on the particle during t = 0 to t = 4 s is

(1)  8 J

(2)  16 J

(3)  32 J

(4)  Zero

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)