Question

Assuming that the potential energy of spring is zero when it is stretched by $x_{0}$ , then its potential energy when it is compressed by $\frac{x_{0}}{2}$ is

• A. $\frac{3}{8}kx_{0}^{2}$
• B. $-\frac{3}{4}kx_{0}^{2}$
• C. $-\frac{3}{8}kx_{0}^{2}$
• D. $\frac{1}{8}kx_{0}^{2}$

Answer 1

Answer: (C)

Change in potential energy is independent of frame of reference.

$\therefore U_{2}- \, U_{1} \, =\frac{1}{2}k\left(\frac{x_{0}}{2}\right)^{2}- \, \frac{1}{2} \, kx_{0}^{2}$
$=-\frac{3}{8}kx_{0}^{2}$