$A$ body of mass $1\, kg$ is moving in a vertical circular path of radius $1\, m$. The difference between the kinetic energies at its highest and lowest position is ......... $J$.

$A$ stone of mass $m$ tied to the end of a string revolves in a vertical circle of radius $R$. The net forces at the lowest and highest points of the circle directed vertically downwards are:

Lowest Point	Highest Point
$(a) \ mg - T_1$	$mg + T_2$
$(b) \ mg + T_1$	$mg - T_2$
$(c) \ mg + T_1 - \frac{mv_1^2}{R}$	$mg - T_2 + \frac{mv_2^2}{R}$
$(d) \ mg - T_1 - \frac{mv_1^2}{R}$	$mg + T_2 + \frac{mv_2^2}{R}$

$T_1$ and $v_1$ denote the tension and speed at the lowest point. $T_2$ and $v_2$ denote corresponding values at the highest point.

$A$ simple pendulum consisting of a light inextensible string of length $\ell$ attached to a heavy small bob of mass $m$ is at rest. The bob is imparted a horizontal impulsive force which gives it a speed of $u = \sqrt{4 g \ell}$. The speed of the bob at its highest point is ($g$ is the acceleration due to gravity).

$A$ ball of mass $2 \,g$ released from the top of an inclined plane describes a circular motion of radius $20 \,cm$ in the vertical plane upon reaching the bottom. The minimum height of the inclined plane is (in $\,cm$)

$A$ smooth inclined plane ends in a vertical circular loop,as shown in the figure. $A$ small body is released from height $h$ as shown. If the body exerts a force of three times its weight on the plane at the highest point of the circle,then the height $h = \alpha R$. The value of $\alpha$ is . . . . . . .

$A$ stone of mass $1 \ kg$ tied to a light inextensible string of length $L = \frac{5}{3} \ m$ is rotating in a circular path of radius $L$ in a vertical plane. If the ratio of maximum tension in the string to the minimum tension in the string is $3$,the speed of the stone at the highest point of the circle is ($g =$ acceleration due to gravity).