AP EAMCET20224 Jul 2022Evening ShiftPhysicsOscillationsActual
A solid sphere of radius R carries a positive charge Q distributed uniformly throughout its volume. A very thin hole is drilled through it's center. A particle of mass m and charge - q performs simple harmonic motion about the center of the sphere in this hole. The frequency of oscillation is
Options
- A1 2 π Q q 4 π ε 0 R 3   m 1 2
- B1 2 π Q q 4 π ε 0 R 2   m 1 2
- C1 2 π Q 4 π ε 0 m R 3 - 1 2
- D1 2 π Q q 4 π ε 0 m R 1 2
Correct answer
A. 1 2 π Q q 4 π ε 0 R 3   m 1 2
Step-by-step solution
Electric field inside a uniformly charged solid sphere is given by, E = Q r 4 π ε 0 R 3 . Therefore, the force on the negative charge - q at distance r from the centre will be F = - Q r q 4 π ε 0 R 3 . Comparing it with F = - k x , k = Q q 4 π ε 0 R 3 . Now the frequency of the oscillation is f = 1 2 π k m = 1 2 π Q q 4 π ε 0 R 3 m .