In the figure below, a neutral insulating disc of mass M and radius R is pivoted at the center. A small charge +q (having negligible mass) is fixed to one edge and a charge of –q (having negligible mass) is fixed to the opposite edge so that line between the two charges makes a small angle $θ$ with an applied uniform electric field $\vec{E}$ as shown. Then (ignore gravity)

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the torque on the disc at the initial moment is $q 2 R E \sin θ$

the angular frequency with which the disc oscillates is $\sqrt{\frac{4 E q}{M R}} .$

the angular frequency with which the disc oscillates is $\sqrt{\frac{2 E q}{M R}} .$

the torque on the disc at the initial moment is $q R E \sin θ$

answer is A, B.

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Detailed Solution

$τ = P E \sin θ = q (2 R) E \sin θ$

$ω = \sqrt{\frac{P E}{I}} = \sqrt{\frac{q (2 R) E}{(M R^{2} / 2)}} = \sqrt{\frac{4 E q}{M R}}$

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