Question

A uniform flexible chain of mass m and length $2\ell$ hangs in equilibrium over a smooth horizontal pin of negligible diameter. One end of the chain slips over the pin. The speed of chain when it leaves pin is

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

Answer 1

The correct option is B $\sqrt{g\ell }$

Decrease in PE$=$ increase in KE
$K=mg(l-\frac{l}{2})\Rightarrow \frac{1}{2}m{v}^2=\frac{mgl}{2}\Rightarrow v=\sqrt{gl}$