$A$ stone of mass $1 \ kg$ is tied to one end of a light string and is whirled in a vertical circle as shown in the figure. The tension in the string when the string becomes horizontal is ......... $N$.

What is the minimum velocity with which a body of mass $m$ must enter a vertical loop of radius $R$ so that it can complete the loop $?$

$A$ 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.

$A$ particle originally at rest at the highest point of a smooth vertical circle is slightly displaced. It will leave the circle at a vertical distance $h$ below the highest point,such that

$A$ ball whose size is slightly smaller than the width of a tube of radius $R = 2.5 \, m$ is projected from the bottommost point of a smooth tube fixed in a vertical plane with a velocity of $v_0 = 10 \, m/s$. Let $N_1$ be the normal reaction exerted by the inner side of the tube and $N_2$ be the normal reaction exerted by the outer side of the tube on the ball. Which of the following statements is correct?

As shown in the figure, a mass $m$ and another block of mass $10m$ are connected with a string of length $L$. Friction is sufficient to prevent the slipping of the $10m$ block. Mass $m$ is given a velocity $u$ in the vertical direction. For the complete circular motion of mass $m$: