$A$ short bar magnet having magnetic moment $4 \text{ Am}^2$,placed in a vibrating magnetometer,vibrates with a time period of $8 \text{ s}$. Another short bar magnet having a magnetic moment $8 \text{ Am}^2$ vibrates with a time period of $6 \text{ s}$. If the moment of inertia of the second magnet is $9 \times 10^{-2} \text{ kg m}^2$,the moment of inertia of the first magnet is (assume that both magnets are kept in the same uniform magnetic induction field.)

• A
  $9 \times 10^{-2} \text{ kg m}^2$
• B
  $8 \times 10^{-2} \text{ kg m}^2$
• C
  $5.33 \times 10^{-2} \text{ kg m}^2$
• D
  $12.2 \times 10^{-2} \text{ kg m}^2$