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 is given a small vertical displacement so that the chain slips over the pin. The speed of chain when it leaves pin is-

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

Answer 1

Answer: (B)

$U _{ i }= M / 2\, g\, \ell / 2+ M / 2 \,g\, \ell / 2=\frac{ Mg \ell}{2}$
$U _{ f }=0$
$w _{ C }=\Delta K$
$\frac{ Mg \ell}{2}-0=1 / 2\, MV ^{2}=0$
$V =\sqrt{ g \ell} \,m / s$