Question

The potential energy of a particle executing $S.H.M$ is $2.5J$.

When its displacement is half of amplitude the total energy of the particle be

• A. 18 J
• B. 15 J
• C. 10 J
• D. 12 J

Answer 1

The correct option is C 10 J

$\begin{array}{c}Weknow,\\ \frac{potentialenergy\left(U\right)}{Totalenergy\left(E\right)}=\frac{\frac{1}{2}m{\omega }^2{y}^2}{\frac{1}{2}m{\omega }^2{a}^2}=\frac{y^2}{a^2}\\ So,\\ \frac{2.5}{E}=\frac{{\left(\frac{a}{2}\right)}^2}{a^2}\\ E=10J\end{array}$