Question

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)	$mg+T_{1}$ $-\left(\frac{mv_{1}^{2}}{R}\right)$	$mg-T_{2}$ $+\left(\frac{mv_{2}^{2}}{R}\right)$
(d)	$mg-T_{1}$ $-\left(\frac{mv_{1}^{2}}{R}\right)$	$mg+T_{2}$ $+\left(\frac{mv_{2}^{2}}{R}\right)$

$T_{1}$ 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. a
• B. b
• C. c
• D. d

Answer 1

Answer: (A)

At the lowest point, mg acts downwards and $T_{1}$
upwards so that net force $=mg$ $-T_{1}$.
At the highest point, both $mg$ and $T_{2}$ act downwards so that net force$=mg$ $+T_{2}.$