A wooden block performs SHM on a frictionless surface with frequency $v_0$. The block carries a charge $+Q$…
A wooden block performs SHM on a frictionless surface with frequency $v_0$. The block carries a charge $+Q$ on its surface. If now a uniform electric field $\mathbf{E}$ is switched on as shown, then the SHM of the block will be
of the same frequency and with shifted mean position
of the same frequency and with the same mean position
of changed frequency and with shifted mean position
of changed frequency and with the same mean position
Solution
Frequency or time period of SHM depends on variable forces. It does not depend on constant external force. Constant external force can only change the mean position. For example, in the given question mean position is at natural length of spring in the absence of electric field. Whereas in the presence of electric field mean position will be obtained after a compression of $x_0$. Where $x_0$ is given by
or
$
\begin{aligned}
k x_0 & =Q E \\
x_0 & =\frac{Q E}{k}
\end{aligned}
$
$\therefore$ Correct answer is (a).
Analysis of Question
(i) Question is simple.
(ii) I think almost all the serious aspirants of JEE can solve this problem easily
