Question

A body of mass $m$ is suspended from a massless spring of natural length $\ell$. It stretches the spring through a vertical distance $y$. The potential energy of the stretched spring is

• A. $mg(\ell +y)$
• B. $\frac{1}{2}mg(\ell +y)$
• C. $\frac{1}{2}mgy$
• D. mgy

Answer 1

The correct option is C $\frac{1}{2}mgy$

At Equilibrium , $ky=mg\Rightarrow k=\frac{mg}{y}$
$U=\frac{1}{2}\left[\frac{mg}{y}\right]y^2=\frac{1}{2}mgy$