First slide

Magnetic dipole in a uniform magnetic field

Question

Magnets A and B are geometrically similar but the magnetic moment of A is twice that of B. If T₁ and T₂be the time periods of the oscillation when their poles and unlike poles are kept together respectively, then $\frac{T_{1}}{T_{2}}$ will be

Easy

A

$\frac{1}{3}$
B

$\frac{1}{2}$
C

$\frac{1}{\sqrt{3}}$
D

$\sqrt{3}$

Solution

We know that $T = 2 π \sqrt{(I / {MB}_{H})}$
$Here, T_{1} = 2 π \sqrt{[\frac{2 I}{(p_{m} + 2 p_{m}) B_{H}}]}$
$and T_{2} = 2 π \sqrt{[\frac{2 I}{(2 p_{m} - p_{m}) B_{H}}]}$
$∴ \frac{T_{1}}{T_{2}} = \frac{1}{\sqrt{3}}$

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