Q164 / 180 · COMEDK 2014 · Physics
A system containing a ball is oscillating on a frictionless horizontal plane. The position of the mass when its potential energy and its kinetic energy both are equal, is (let $A$ is the amplitude of oscillation)
- A$A$
- Correct answerB$A / \sqrt{2}$
- C$A / 2$
- D$A / \sqrt{3}$
Solution
Kinetic energy of the system in SHM,
$$
\mathrm{KE}=\frac{1}{2} m \omega^{2}\left(A^{2}-x^{2}\right)
$$
Potential energy of the system in $\mathrm{SHM}, \mathrm{PE}=\frac{1}{2} m \omega^{2} x^{2}$
According to question, $\mathrm{PE}=\mathrm{KE}$
$$
\begin{aligned}
\frac{1}{2} m \omega^{2} x^{2} &=\frac{1}{2} m \omega^{2}\left(A^{2}-x^{2}\right) \\
\Rightarrow \quad x^{2} &=A^{2}-x^{2} \\
\Rightarrow \quad 2 x^{2}=A^{2} \Rightarrow x &=\frac{A}{\sqrt{2}}
\end{aligned}
$$
Hence, the correct answer is option: 'B'.