Question

A spring of natural length $l$ is compressed vertically downward against the floor so that its compressed length becomes $\frac{l}{2}$. On releasing, the spring attains it's natural length. If $k$ is the stiffness constant of the spring, then the work done by the spring on the floor is

• A. $zero$
• B. $\frac{1}{2}k{l}^2$
• C. $\frac{1}{2}k(\frac{l}{2}{)}^2$
• D. $k{l}^2$

Answer 1

The correct option is A $zero$

Only the center of mass of the spring changes, but the floor has no displacement.
$W=F.x$
$W=F\times 0$
$W=0$
Hence the work done by the spring on the floor is zero.
Option A.