Q. The potential energy of a particle executing S.H.M. is $2.5\ J,$ when its displacement is half of amplitude. The total energy of the particle be
A) $18\ J$
B) $10\ J$
C) $12\ J$
D) $2.5\ J$
Explanation
(b) $\frac{Potential\ energy\ (U)}{Total\ energy\ (E)} = \frac{\frac{1}{2}m\omega^{2}y^{2}}{\frac{1}{2}m\omega^{2}a^{2}} = \frac{y^{2}}{a^{2}}$
$So\ \frac{2.5}{E} = \frac{\left( \frac{a}{2} \right)^{2}}{a^{2}} \Rightarrow E = 10J$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.