A ball is allowed to fall from a height of 10 m. If there is a 40% loss of energy due to impact, then after one impact ball will go up by

(1)  10 m

(2)  8 m

(3)  4 m

(4)  6 m

A particle of mass m is moving with velocity $\overrightarrow{\mathrm{v}} = \left(4\hat{\mathrm{i}} - 6\hat{\mathrm{j}}\right)$ m/s collides on a horizontal smooth surface as shown. If the coefficient of restitution is  $\mathrm{e} = \frac{1}{2}$, then the velocity of the particle after the collision is

1.  $\overrightarrow{\mathrm{v}} = \left(4\hat{\mathrm{i}} - 3\hat{\mathrm{j}}\right)$ m/s

2.  $\overrightarrow{\mathrm{v}} = \left(4\hat{\mathrm{i}} + 3\hat{\mathrm{j}}\right)$ m/s

3.  $\overrightarrow{\mathrm{v}} = \left(2\hat{\mathrm{i}} - 3\hat{\mathrm{j}}\right)$ m/s

4.  $\overrightarrow{\mathrm{v}} = \left(2\hat{\mathrm{i}} + 3\hat{\mathrm{j}}\right)$ m/s

A sphere moving with speed u collides elastically with another identical sphere at rest. If the collision is not head-on, then the angle between their final velocities is

(1)  0°

(2)  60°

(3)  90°

(4)  45°

In a conservative field, work is done on a body by the field, then

(1)  The kinetic energy of the body definitely increases.

(2)  The kinetic energy of the body decreases.

(3)  The potential energy of the body increases.

(4)  Potential energy of the body decreases.

Work is done by an agent applying force when

(1)  the applied force is variable.

(2)  the applied force is perpendicular to the motion.

(3)  the applied force generate motion.

(4)  the applied force is constant.

A ball is let to fall from a height of 32 m on the ground. The coefficient of restitution is $\mathrm{e} = \frac{1}{2}$. The height raised by the ball after the second rebound is

(1)  2 m

(2)  4 m

(3)  8 m

(4)  16 m

A bob of a simple pendulum is released from position A. Velocity of the bob when it is at lowest position A is

(1)  $\sqrt{50}$ m/s

(2)  10 m/s

(3)  5 m/s

(4)  2$\sqrt{5}$ m/s

A bob is suspended from a peg on a wall by a massless string of length L. If it is given velocity $\sqrt{2gL}$ at the lowest point, then angular amplitude with which body will oscillate is

(1)  60°

(2)  90°

(3)  75°

(4)  30°

The ratio of the kinetic energy of a particle projected from the ground at the  highest point to point of projection is 1/4. The angle of projection with horizontal is

(1)  30°

(2)  60°

(3)  45°

(4)  53°

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration ${\mathrm{a}}_{\mathrm{r}}$ is varying with time t as ${\mathrm{krt}}^2$,where k is constant. The power delivered to the particle by the force acting on it is

(1)  $2{\mathrm{\pi kmr}}^2$

(2)  ${\mathrm{kmr}}^2\mathrm{t}$

(3)  ${\mathrm{kmr}}^2{\mathrm{t}}^5$

(4)  Zero