Question

A uniform chain of mass '$m$' is placed over half ring. If the length of the chain is $\pi R$, then find potential energy of the chain.

• A. $\frac{mgR}{2}$
• B. $mgR$
• C. $\frac{2mgR}{\pi }$
• D. $\frac{4mgR}{3\pi }$

Answer 1

The correct option is C $\frac{2mgR}{\pi }$

We know that, the potential energy is calculated by:
$PE=mgh$
'$h$' here represents the distance of the center of mass from the zero potential energy line.
In case of a half ring, its center of mass lies at a distance of $2R/\pi$ from its center.
So, in this case, we get $h=2R/\pi$

$\therefore PE=mg\frac{2R}{\pi }=\frac{2mgR}{\pi }$