$A$ 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) At the lowest point,the forces acting on the stone are the tension $T_1$ acting upwards and the weight $mg$ acting downwards. The net force directed towards the center (upwards) is $T_1 - mg = \frac{mv_1^2}{R}$. The net force directed vertically downwards is $mg - T_1 = -\frac{mv_1^2}{R}$.
At the highest point,both the tension $T_2$ and the weight $mg$ act downwards. The net force directed vertically downwards is $mg + T_2 = \frac{mv_2^2}{R}$.
Comparing these with the options provided,the question asks for the net force directed vertically downwards. For the lowest point,this is $mg - T_1$. For the highest point,this is $mg + T_2$. Thus,option $(a)$ is correct.