A body is executing S.H.M. Its potential energy is ' $\mathrm{P}_1$ ' and ' $\mathrm{P}_2$ ' at displacements ' $x$ ' and ' $y$ ' respectively. The potential energy at displacement $(\mathrm{x}+\mathrm{y})$ is

• A

  $\sqrt{\mathrm{P}_1}-\sqrt{\mathrm{P}_2}=\sqrt{\mathrm{p}}$
• B

  $\mathrm{p}_1+\mathrm{p}_2=\mathrm{p}$
• C

  $\mathrm{p}_1-\mathrm{p}_2=\mathrm{p}$
• Correct answer
  D

  $\sqrt{\mathrm{p}_1}+\sqrt{\mathrm{p}_2}=\sqrt{\mathrm{p}}$

Solution

At displacement $\mathrm{x}$ At displacement y $\mathrm{E}_1=\frac{1}{2} \mathrm{~m} \omega^2 \mathrm{x}^2$ From equations (1), Or (2) and (3) it follows that $\sqrt{\mathrm{E}}=\sqrt{\mathrm{E}_1}+\sqrt{\mathrm{E}_2}$ Or $\mathrm{E}=\mathrm{E}_1+\mathrm{E}_2+2 \sqrt{\mathrm{E}_1 \mathrm{E}_2}$

Hence, the correct answer is option: 'D'.