Question

A body crosses the topmost point of a vertical circle with critical speed. What will be its centripetal acceleration when the string is horizontal. :-

• A. $g$
• B. $2g$
• C. $3g$
• D. $6g$

Answer 1

The correct option is C $3g$

The critical speed of the body at the topmost point is equal to $\sqrt{gR}$ i.e $v=\sqrt{gR}$

Let the velocity of the body when the string is horizontal be $v_2$

Using work-energy theorem : $W=\Delta K.E$

$\therefore$ $mgR=\frac{1}{2}m{v}_2^2-\frac{1}{2}m{v}^2$

OR $mgR=\frac{1}{2}m{v}_2^2-\frac{1}{2}m\left(gR\right)$ $⟹v_2^2=3gR$

Centripetal acceleration $a_r=\frac{v_2^2}{R}=3g$