Question

A body is tied at the end of a string of length L and revolved in a vertical circle. The string is just taut when the body is at the highest position. Velocity of the body when the string is horizontal is

• A. $3gL$
• B. $L$
• C. $\sqrt{5gl}$
• D. $\sqrt{3gl}$

Answer 1

Answer: (D)

$\sqrt{3gl}$

Apply energy conservation between top and horizontal point

Velocity at highest point $=\sqrt{gl}$

$\frac{1}{2}m{v}_2^2-\frac{1}{2}m{v}_1^2=mg\left(h\right)$

$\Rightarrow \frac{1}{2}m{v}_2^2-\frac{1}{2}m\left(gL\right)=mg\left(L\right)$

$\Rightarrow V_2^2=3gL$

$V=\sqrt{3gL}$