$A$ bar magnet has a magnetic moment equal to $5 \times 10^{-5} \, \text{Wb} \cdot \text{m}$. It is suspended in a magnetic field which has a magnetic induction $B$ equal to $8\pi \times 10^{-4} \, \text{T}$. The magnet vibrates with a period of vibration equal to $15 \, \text{s}$. The moment of inertia of the magnet is:

  • A
    $22.5 \, \text{kg} \cdot \text{m}^2$
  • B
    $11.25 \, \text{kg} \cdot \text{m}^2$
  • C
    $5.62 \, \text{kg} \cdot \text{m}^2$
  • D
    $7.16 \times 10^{-7} \, \text{kg} \cdot \text{m}^2$

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$A$ thin rectangular magnet suspended freely has a period of oscillation equal to $T$. Now it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely in the same field. If its period of oscillation is $T'$,the ratio $T'/T$ is :-

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