A body is released from the top of an inclined smooth plane of inclination $\mathrm{\theta }$. It reaches the bottom with speed u. If the angle of inclination is doubled keeping the height unchanged, then the speed of the object on reaching on the ground is

(1)  u

(2)  2u

(3)  $\mathrm{u}\sqrt{2\cos \mathrm{\theta }}$

(4)  $\frac{\mathrm{u}}{\sqrt{2\sin \mathrm{\theta }}}$

Select the correct statement. Work is done by the internal forces on the system

(1)  maybe zero.

(2)  must be greater than zero.

(3)  must be less than zero.

(4)  must be zero.

A block of mass m is attached with a spring of spring constant k as shown in the figure. Another block of mass 2m moving with speed v hits the spring. Speed of blocks at the instant of maximum compression of spring is:

1.  $\frac{\mathrm{v}}{3}$

2.  $\frac{\mathrm{v}}{2}$

3.  $\frac{2\mathrm{v}}{3}$

4.  $\frac{3\mathrm{v}}{2}$

The potential energy of a particle of mass m varies as $U=a{x}^2+by.$ The magnitude of the acceleration of the particle at (0, 3) is (symbols have their usual meaning)

1.  $\sqrt{\frac{\mathrm{b}}{\mathrm{m}}}$

2.  $\sqrt{\frac{3\mathrm{b}}{\mathrm{m}}}$

3.  $\frac{\mathrm{b}}{\mathrm{m}}$

4.  Zero

A ball of mass 100 g at rest is thrown on a horizontal surface as shown in the figure. The acceleration-displacement graph for the motion is given. The maximum height attained by the ball on the smooth inclined plane is

(1)  10 m

(2)  4 m

(3)  2 m

(4)  1 m

A body moving with speed 10 m/s is stopped by applying constant braking power in 5 seconds. If the speed of the body is 30 m/s, then time in which the body can be stopped by applying the same retarding power is

(1)  10 s

(2)  15 s

(3)  30 s

(4)  45 s

A small ball is given a velocity $\sqrt{2gl}$ on the smooth horizontal floor which leads to a smooth vertical circular path. The ball will Smooth

(1)  complete the loop.

(2)  reach only up to point P.

(3)  reach to point Q.

(4)  leave the contact somewhere between P and Q.

A vertically compressed spring of constant k releases a ball of mass m as shown in the figure. The maximum height attained by the ball from the compressed point is (x is the initial compression in the spring)

1.  $\frac{{\mathrm{kx}}^2}{2\mathrm{mg}}$

2.  $\frac{{\mathrm{kx}}^2}{\mathrm{mg}}$

3.  $\frac{{\mathrm{kx}}^2}{4\mathrm{mg}}$

4.  $\frac{2{\mathrm{kx}}^2}{\mathrm{mg}}$