Question

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

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

Answer 1

Answer: (A)

Change in potential energy is independent of reference

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