Question

A stone attached to a string is rotated in a vertical circle such that when it is at the top of the circle its speed is $V$ and there is neither tension nor slacking in the string. The speed of stone when it's angular displacement is ${120}^{\circ }$ from the lowest point is

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

Answer 1

Answer: (B)

$\sqrt{2}V$

at foremost point
$mg$ $=\frac{m{v}^2}{R}$

$V=\sqrt{Rg}$
also $H$$=R(1-cos{60}^0)=\frac{R}{2}$
Using conservation of energy
$\frac{1}{2}m{V}^2=\frac{1}{2}m{V}_1^2-mg\frac{R}{2}.$
$\frac{mRg+mRg}{2}=\frac{m}{2}V{{}_1}^2.$
$2Rg=V_1$

$\sqrt{2Rg}=V_1$

$\sqrt{2}V=V_1$