Magnetism and Matter · Question 33

A bar magnet is oscillating in the Earth's magnetic field with a period T. What happens to its period and motion if its mass is quadrupled?

1. motion remains simple harmonic with time period = T2
2. motion remains S.H.M. with time period = 2T
3. motion remains S.H.M. with time period = 4T
4. motion remains S.H.M. and period remains nearly constant

Answer

(2) motion remains S.H.M. with time period = 2T

Solution

For small oscillations of a bar magnet in a uniform field B, the restoring torque is = -mB , so the motion is simple harmonic with

T = 2 ImB (m = magnetic moment)

∵ Moment of inertia I mass, quadrupling the mass makes I' = 4I (m and B unchanged).

⇒ T' = 2 4ImB = 2T

∴ The motion remains S.H.M. and the period becomes 2T.

Answer: (2)