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Electrostatics question

2024 · Shift 2 · Q39
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Electrostatics question

2024 · Shift 2 · Q39

JEE AdvancedPhysicsElectrostaticsMultiple correct+4 / −2
A small electric dipole p⃗0\vec{p}_0p​0​, having a moment of inertia III about its center, is kept at a distance rrr from the center of a spherical shell of radius RRR. The surface charge density σ\sigmaσ is uniformly distributed on the spherical shell. The dipole is initially oriented at a small angle θ\thetaθ as shown in the figure. While staying at a distance rrr, the dipole is free to rotate about its center. JEE Advanced 2024 Paper 2 Online Physics - Electrostatics Question 7 English If released from rest, then which of the following statement(s) is(are) correct? [ ε0\varepsilon_0ε0​ is the permittivity of free space.]
  1. A
    The dipole will undergo small oscillations at any finite value of rrr.
  2. B
    The dipole will undergo small oscillations at any finite value of r>Rr>Rr>R.
  3. C
    The dipole will undergo small oscillations with an angular frequency of 2σp0ϵ0I\sqrt{\frac{2 \sigma p_0}{\epsilon_0 I}}ϵ0​I2σp0​​​ at r=2Rr=2 Rr=2R.
  4. D
    The dipole will undergo small oscillations with an angular frequency of σp0100ϵ0I\sqrt{\frac{\sigma p_0}{100 \epsilon_0 I}}100ϵ0​Iσp0​​​ at r=10Rr=10 Rr=10R.
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