Question

A mass $m$ is attached to the end of a rod of length $\ell$. The mass goes around a verticle circular path with the other end hinged at the centre. What should be the minimum velocity of mass at the bottom of the circle so that the mass completes the circle?

• A. $\sqrt{4g\ell }$
• B. $\sqrt{3g\ell }$
• C. $\sqrt{5g\ell }$
• D. $\sqrt{g\ell }$

Answer 1

Answer: (A)

$\sqrt{4g\ell }$

At top most point speed of the body may be zero because rod will support the body there.
Applying energy conservation at lowest point, $\frac{1}{2}m{v}^2=0+mg\left(2l\right)$
or $v=\sqrt{4gl}$