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

Question

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

Tardigrade Admin · Accepted Answer

Change in potential energy is independent of reference
Solution

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

Q. 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

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

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

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

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

Change in potential energy is independent of reference

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

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

83​kx02​

−43​kx02​

43​kx02​ ​

81​kx02​