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A small electric dipole p ₀ , having a moment of inertia I about its center, is kept at a distance r from the center of a spherical shell of radius R . The surface charge density is uniformly distributed on the spherical shell. The dipole is initially oriented at a small angle as shown in the figure. While staying at a distance r , the dipole is free to rotate about its center. If released from rest, then which of th

Options

  1. AThe dipole will undergo small oscillations at any finite value of r .
  2. BThe dipole will undergo small oscillations at any finite value of r>R .
  3. CThe dipole will undergo small oscillations with an angular frequency of 2 p₀ ₀ I at r=2 R .
  4. DThe dipole will undergo small oscillations with an angular frequency of p₀ 100 ₀ I at r=10 R .

Correct answer

B. The dipole will undergo small oscillations at any finite value of r>R .

Step-by-step solution

( aligned & =| p E | & I =p₀ E & = p I ( 1 4 ₀ 4 R^2 r^2 ) & = ( p 0 R^2 I ₀ r^2 ) & = p 0 R^2 I ₀ r^2 aligned ) For (r=2 R ) ( = p₀ 4 / ₀ ( C ) is incorrect () ) Also, for (r=10 R ) ( = p₀ 4 l(100) ) (D is correct) It will oscillate for any finite value of (r>R ). (B is correct)

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