Two magnetic bars are suspended in horizontal plane and ocillates in earth magnetic field. Their time period of oscillations are $T_{1}$ and $T_{2}$ . The ratio of their magnetic dipole moments is :

\frac{T_{1}}{T_{2}}

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\frac{T_{2}}{T_{1}}

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{(\frac{T_{1}}{T_{2}})}^{2}

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{(\frac{T_{2}}{T_{1}})}^{2}

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Solution

The correct option is D ${(\frac{T_{2}}{T_{1}})}^{2}$
Given :
Time period of two magnetic bars as $T_{1}$ and $T_{2}$ .

Solution:
From angular SHM and torque relation $τ = - \to M \times \to B$
Time period of oscillation is given as : $T = 2 π \sqrt{\frac{I}{M B}}$
So, $T α \sqrt{\frac{1}{M}}$

So, $\frac{T_{1}}{T_{2}} = \sqrt{\frac{M_{2}}{M_{1}}}$

Square both sides,
Hence, $\frac{M_{1}}{M_{2}} = {(\frac{T_{2}}{T_{1}})}^{2}$

Correct Opt:[D]

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