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

Work done the spring force in a time interval maybe

(1)  Positive

(2)  Negative

(3)  Zero

(4)  All of these

A body of mass m moving with velocity v in X-direction collides with another identical body moving with the same speed in the y-direction. They coalesce into one body during a collision. The direction of motion of the composite body after the collision is

(1)  30' with X-axis

(2)  45° with X-axis

(3)  60° with X-axis

(4)  Along the y-axis

 A ball of mass m at rest starts moving from point A. The irregular surface is frictionless. The speed of the ball at the point C on the track is

1.  $\sqrt{\frac{4\mathrm{gH}}{3}}$

2.  $\sqrt{\frac{2\mathrm{gH}}{3}}$

3.  $\sqrt{\mathrm{gH}}$

4.  Zero

A ball strikes the floor and rebounds after an inelastic collision. Which of the following is correct?

(1)  The total momentum of the earth and ball system is conserved.

(2)  The total mechanical energy of the ball and earth system is conserved.

(3)  The momentum of the ball is conserved.

(4)  Both (1) & (2)