A tin rectangular magnet suspended freely has a period of oscillation equal to $T$ . Now it is broken into equal halves (each having half of the original length) and one piece is mode to oscillate freely in the same field. If its period of oscillation is $T^{'}$ , the ratio $\frac{T ^{'}}{T}$ is :

Question

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Answer 1

$m =$ mass of rectangular magnet
$M =$ Magnetic moment

Moment of inertia, $I_{1} \propto l^{2} m$
Time period, T $\propto \frac{I}{M}$
Therefore, time period $T \propto l \times \frac{m}{M}$
when magnet is cut then mass and magnetic moment becomes half.
Hence, time period becomes half
Option B is answer.

Answer 2

m =

mass of rectangular magnet

M =

Magnetic moment

Moment of inertia,

I_{1} \propto l^{2} m

Time period, T

\propto \frac{I}{M}

Therefore, time period

T \propto l \times \frac{m}{M}

when magnet is cut then mass and magnetic moment becomes half.

Hence, time period becomes half

Option B is answer.