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MHT CET 2023 (11 May, Shift 1) · Motion of Charges in an Electric Field

Motion of Charges in an Electric Field question from MHT CET 2023 (11 May, Shift 1)

Q18MHT CET 2023 · 11 MAY · SHIFT 1Medium

Motion of Charges in an Electric Field

The bob of a simple pendulum of length ' $L$ ' has a mass ' $m$ ' and charge ' $q$ '. The pendulum is suspended between the plates of a charged parallel plate capacitor. The direction of electric field is shown in figure. The period of oscillations of the simple pendulum is (acceleration due to gravity $g > qE/m$ )

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Answer: (c)

$\vec{E}$ is upward, so the force $qE$ on the (positive) bob is upward, opposite to gravity.
Effective gravity: $g_{\text{eff}} = g - \frac{qE}{m}$ (positive since $g > \frac{qE}{m}$ ).
$T = 2\pi\sqrt{\frac{L}{g - \frac{qE}{m}}}$
So the answer is (c).

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