Question

A frictionless pulley has radius r. A uniform chain of linear density d and total length $(2L+\pi r)$ is released from rest over the pulley as shown. When right end is lowered by $y=y_0$ from the mean position, speed of the chain is

• A. ${\left[\frac{2g{y}^2}{2L+\pi r}\right]}^{\frac{1}{2}}$
• B. ${\left(\frac{1}{2}g\frac{y^2}{L}\right)}^{\frac{1}{2}}$
• C. ${\left[\frac{g{y}^2}{L+\pi r}\right]}^{\frac{1}{2}}$
• D. None of these

Answer 1

The correct option is A

${\left[\frac{2g{y}^2}{2L+\pi r}\right]}^{\frac{1}{2}}$

By law of conservation of energy $\frac{1}{2}m{v}^2=dg{y}_0^2$

Putting $m=(2L+\pi R)d$, we get

$v=\sqrt{\frac{2g{y}_0^2}{2L+\pi R}}$