Question

The total mechanical energy of a particle of mass m executing SHM is $E=\left(1/2\right)m{\omega }^2{A}^2.$ If the particle is replaced by another particle of mass m/2 while the amplitude A remains same. New mechanical energy will be

• A. $\sqrt{2}E$
• B. 2E
• C. E/2
• D. E

Answer 1

The correct option is D E

In SHM $\omega =\sqrt{\frac{k}{m}}$

$E=\frac{1}{2}m{\omega }^2{A}^2$

Substituting the value of $\omega$

$E=\frac{1}{2}m\frac{k}{m}{A}^2$

$E=\frac{1}{2}k{A}^2$

Hence we can clearly see that energy $E$ is independent of mass

So if maas $m$ is replaced by a mass $\frac{m}{2}$

Energy will remain same $E$