Simple Harmonic Motion 4 Question 6
6. 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
(2011)
(a) of the same frequency and with shifted mean position
(b) of the same frequency and with the same mean position
(c) of changed frequency and with shifted mean position
(d) of changed frequency and with the same mean position
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Answer:
Correct Answer: 6. (a)
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
$$ K x _0=Q E \text { or } x _0=\frac{Q E}{K} $$
$\therefore$ Correct answer is (a).
