First slide

Magnetic dipole in a uniform magnetic field

Question

The time period of a magnet ( when behaving like a compound pendulum) is T. The bar magnet is cut into 4 equal parts by cutting it normal to its length. The time period of each of them in the same field is

Moderate

A

T
B

T/2
C

T/4
D

2T

Solution

$T = 2 π \sqrt{\frac{I}{M . B}}, So$
$\begin{array}{l} \frac{T_{1}}{T_{2}} = \sqrt{\frac{I_{1}}{I_{2}} . \frac{M_{2}}{M_{1}}} = \sqrt{\frac{64}{1} . \frac{1}{4}} = \frac{4}{1} \\ \Rightarrow T_{2} = \frac{T_{1}}{4} \end{array}$

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