Question

A particle is moving along a vertical circle of radius $R$. At $P$, what will be the velocity of particle (assume critical condition at $C)$ ?

• A. $\sqrt{gR}$
• B. $\sqrt{2gR}$
• C. $\sqrt{3gR}$
• D. $\sqrt{\frac{3}{2}gR}$

Answer 1

Answer: (B)

At critical condition at $C$
$v=\sqrt{gR}$
Using mechanical energy conservation between points $P$ and $C$ (taking P.E. $=0$ at $P$ )
$U_i+k_i=U_f+k_f$
$0+\frac{1}{2}m{v}^2=mgR\left(1-\cos 60^{\circ }\right)+\frac{1}{2}m(\sqrt{gR}{)}^2$
$\frac{1}{2}m{v}^2=\frac{mgR}{2}+\frac{mgR}{2}$
$v=\sqrt{2gR}$