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Q.

At the center of a hollow hemisphere uniformly charged with a surface charge density σ, there is a small dipole of dipole moment ρ. The moment of inertia about the rotation axis is I.

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a

The magnitude of E due to hemisphere at the center of hemisphere is σ20

b

The minimum potential energy of dipole is ρσ40

c

The dipole performs SHM for small angular displacements with angular frequency is ω=ρEI

d

If dipole is released from rest from a position perpendicular to the symmetry axis, the maximum KE of dipole is σρ40

answer is B, C, D.

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Detailed Solution

 Question Image
(A) E at center =σ40  
(B) U=ρE=σ40ρ  
(C) σρ40+KE=0  
KE=σρ40 
(D) Iα=ρEθ  
α=ρEIθ 
ω=ρEI  

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