Question

A body is executing S.H.M. at a displacement $x$, its P.E. is $E_1$ and at a displacement $y$ its P.E. is $E_2$. The P.E. at displacement $(x+y)$ is

• A. $\sqrt{E}$ = $\sqrt{E_1}$ - $\sqrt{E_2}$
• B. $\sqrt{E}$ = $\sqrt{E_1}$ + $\sqrt{E_2}$
• C. $E=E_1+E_2$
• D. $E=E_1-E_2$

Answer 1

Answer: (B)

$\sqrt{E}$ = $\sqrt{E_1}$ + $\sqrt{E_2}$

$PE=\frac{1}{2}k{x}^2$
$E_1=\frac{1}{2}k{x}^2$
$E_2=\frac{1}{2}k{g}^2$
$E=\frac{1}{2}k(x+y{)}^2$
$x+y=\sqrt{\frac{2E}{K}}$
$\sqrt{\frac{2E_1}{K}}+\sqrt{\frac{2E_2}{K}}=\sqrt{\frac{2E}{K}}$
$\sqrt{E}=\sqrt{E_1}+\sqrt{E_2}$