Assuming that the potential energy of spring is zero when it is stretched by x0 , then its potential energy when it is compressed by (x0/2) is

Question

Assuming that the potential energy of spring is zero when it is stretched by x0 , then its potential energy when it is compressed by (x0/2) is (A) (3/8)kx02 (B) -(3/4)kx02 (C) -(3/8)kx02 (D) (1/8)kx02

Tardigrade Admin · Accepted Answer

Change in potential energy is independent of frame of reference.
Solution

∴ U_{2} - U_{1} = \frac{1}{2} k (\frac{x _{0}}{2})^{2} - \frac{1}{2} k x_{0}^{2}

= - \frac{3}{8} k x_{0}^{2}

Q. 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

$\frac{3}{8} k x_{0}^{2}$

$- \frac{3}{4} k x_{0}^{2}$

$- \frac{3}{8} k x_{0}^{2}$

$\frac{1}{8} k x_{0}^{2}$

Change in potential energy is independent of frame of reference.

$∴ U_{2} - U_{1} = \frac{1}{2} k (\frac{x _{0}}{2})^{2} - \frac{1}{2} k x_{0}^{2}$
$= - \frac{3}{8} k x_{0}^{2}$

Q. Assuming that the potential energy of spring is zero when it is stretched by x0​ , then its potential energy when it is compressed by 2x0​​ is

83​kx02​

−43​kx02​

−83​kx02​

81​kx02​