The kinetic energy of a body is increased by 21%. The percentage increase in the magnitude of linear momentum of the body will be:

1.  10%

2.  20%

3.  Zero

4.  11.5%

A rigid body of mass \(\mathrm{m}\) is moving in a circle of radius \(\mathrm{r}\) with constant speed \(\mathrm{v}.\) The force on the body is $\frac{{\mathrm{mv}}^2}{\mathrm{r}}$ and is always directed towards the center. The work done by this force in moving the body over half the circumference of the circle will be:
1. $\frac{{\mathrm{mv}}^2}{\mathrm{r\pi }}$ 
2. ${\mathrm{mr}}^2\mathrm{\pi }$
3. zero
4. $2{\mathrm{mv}}^2\mathrm{\pi }$

A block is released from rest from a height of h = 5 m. After travelling through the smooth curved surface, it moves on the rough horizontal surface through a length l = 8 m and climbs onto the other smooth curved surface at a height h'. If $\mathrm{\mu }$ = 0.5, find h'.

A body initially at rest and sliding along a frictionless track from a height h (as shown in the figure) just completes a vertical circle of diameter AB = D. The height h is equal to: 
            

1. $\frac{3}{2}D$

2. D

3. $\frac{7}{4}D$

4. $\frac{5}{4}D$

When a spring is subjected to 4 N force, its length is a metre and if 5 N is applied, its length is b metre. If 9 N is applied, its length will be:

1.  4b – 3a

2.  5b – a

3.  5b – 4a

4.  5b – 2a

A mass of \(0.5\) kg moving with a speed of \(1.5\) m/s on a horizontal smooth surface, collides with a nearly weightless spring with force constant \(k=50\) N/m. The maximum compression of the spring would be:
           
1.  \(0.12\) m
2.  \(1.5\) m
3.  \(0.5\) m
4.  \(0.15\) m

A ball is dropped from a height of \(5\) m. If it rebounds up to a height of \(1.8\) m, then the ratio of velocities of the ball after and before the rebound will be:
1. $\frac{3}{5}$

2. $\frac{2}{5}$

3. $\frac{1}{5}$

4. $\frac{4}{5}$ 

The bob of a simple pendulum having length l, is displaced from the mean position to an angular position θ with respect to vertical. If it is released, then the velocity of the bob at the lowest position will be:

1. $\sqrt{2gl(1-\cos \theta )}$

2. $\sqrt{2gl(1+\cos }$ $\theta )$

3. $\sqrt{2gl}$ $\cos \theta$

4. $\sqrt{2gl}$

A block of mass \(m\) is being lowered by means of a string attached to it. The system moves down with a constant velocity. Then:
                                         
1. Work done by gravity on the block is positive.

2. Work done by F (the force of the string) on the block is negative.

3. Work done by gravity is equal in magnitude to that done by the string.

4. All of the above are true.

A body constrained to move along the \(\mathrm{z}\)-axis of a coordinate system is subjected to constant force given by \(\vec{F}=-\hat{i}+2 \hat{j}+3 \hat{k}\) where \(\hat{i},\hat{j} \) and \(\hat{k}\) are unit vectors along the \(\mathrm{x}\)-axis, \(\mathrm{y}\)-axis and \(\mathrm{z}\)-axis of the system respectively. The work done by this force in moving the body a distance of \(4\) m along the \(\mathrm{z}\)-axis will be:
1. \(15\) J
2. \(14\) J
3. \(13\) J
4. \(12\) J