Question

The time period of a vibration magnetometer is $T_0$. Its magnet is replaced by another magnet whose moment of inertia is 3 times and magnetic moment is $\frac{1}{3}$ of the initial magnet. The time period now will be :

• A. $3T_0$
• B. $T_0$
• C. $\frac{T_0}{\sqrt{3}}$
• D. $\frac{T_0}{3}$

Answer 1

The correct option is A $3T_0$

The time period of oscillation is given by
$T_0=2\pi \sqrt{\frac{I_0}{MB}}$
$I_1=3I_0$
$M_1=\frac{M_0}{3}$
$\frac{T_1}{T_0}=\sqrt{\frac{I_1{M}_0}{I_0{M}_1}}$
$T_1=3T_0$