Question

A smooth chain PQ of mass $M$ rests against a ${\frac{1}{4}}^{th}$ circular and smooth surface of radius $r$. If released, its velocity to come over the horizontal part of the surface is

• A. $\sqrt{2gr}\times \frac{1}{4}$
• B. $\sqrt{2gr(1-\frac{1}{\pi })}$
• C. $\sqrt{2gr(1-\frac{2}{\pi })}$
• D. $\sqrt{gr(1-\frac{2}{\pi })}$

Answer 1

The correct option is C $\sqrt{2gr(1-\frac{2}{\pi })}$

Work done $=\Delta KE$,
$Mg(r-\frac{2r}{\pi })=\frac{1}{2}M{v}^2$
($\because$ of c.g. of the chain)
or $u=\sqrt{2gr(1-\frac{2}{\pi })}$