Question

A ball of mass $m$ is attached to one end of a light rod of length $l$, the other end of which is hinged. What minimum velocity $v$ should be imparted to the ball downwards, so that it can complete the circle?

• A. $\sqrt{gl}$
• B. $\sqrt{3gl}$
• C. $\sqrt{2gl}$
• D. $\sqrt{4gl}$

Answer 1

The correct option is C $\sqrt{2gl}$

Answer (2)


For required condition
$v\ge \sqrt{4gl}$
Using energy conservation
$mgl+\frac{1}{2}m{u}^2\ge \frac{1}{2}m{v}^2$
$u^2\ge 4gl-2gl$
$u\ge \sqrt{2gl}$
$u_{\text{min}}=\sqrt{2gl}$