First slide

Magnetic dipole in a uniform magnetic field

Question

The ratio of time periods of oscillation of two magnets of same moment of inertia suspended in a magnetic field is 1 : 2. The ratio of their magnetic moments is

Moderate

A

4 : 1
B

1 : 4
C

$\sqrt{2} : 1$
D

$1 : \sqrt{2}$

Solution

$\begin{array}{l} T = 2 π \sqrt{(I / MB)} \\ T^{'} = 2 π \sqrt{(I / M^{'} B)} \\ ∴ {(\frac{T}{T^{'}})}^{2} = \frac{M^{'}}{M} or {(\frac{1}{2})}^{2} = \frac{M^{'}}{M} \\ or \frac{M}{M^{'}} = \frac{4}{1} \end{array}$

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