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Free Body Diagram

A particle of...

Question

A particle of mass $m$ and charge $q$ is attached to a light rod of length $L$ . The rod can rotate freely in the plane of paper about the other end, which is hinged at $P$ . The entire assembly lies in a uniform electric field $E$ also acting in the plane of paper as shown. The rod is released from rest when it makes an angle $θ$ with the electric field direction. (Assume gravity free speace)

θ

is small, the particle performs

S H M

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The speed of the particle when the rod is parallel to the electric field is

{(\frac{2 q E L (1 - sin θ)}{m})}^{\frac{1}{2}}

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The speed of the particle when the rod is parallel to the electric field is

{(\frac{2 q E L (1 - cos θ)}{m})}^{\frac{1}{2}}

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Direction of angular acceleration changes alternatively

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Solution

The correct option is D Direction of angular acceleration changes alternatively
Since electric field iis rightwards $A$ is at hightest potential
$V_{A} - V_{B} = (E) (A ‘ B)$
$= E l (1 - cos θ) = E l (1 - cos θ)$
$U_{A} - U_{B} = q (_{A} - V_{B})$
$= \frac{1}{2} m v^{2} - \frac{1}{2} m v_{0}^{2}$

$E l (1 - cos θ) (q) = \frac{1}{2} m v^{2}$
$v = {(\frac{2 q E l (1 - cos θ)}{m})}^{\frac{1}{2}}$
For small $θ$ , oscillation is $S H M$

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