Question

The periodic time of a magnet in vibration magnetometer is \(T_0\). If a magnet is replaced by another magnet whose moment of inertia is three times and magnetic moment is one-third of the original magnet, then time period of new magnet will be

• A. \(\frac{T_0}{3}\)
• B. \(\frac{T_0}{\sqrt{3}}\)
• C. \(3\,T_0\)
• D. \(\sqrt{3}\,T_0\)

Hint:

T = 2 pi sqrt(I / (M B)).

Answer 1

The Correct Option is C

Step 1: Look at the ratio I/M:
$T \propto \sqrt{\frac IM}$.

Step 2: Factor:
$\frac{I'}{M'} = \frac{3I}{M/3} = 9\frac IM$.

Step 3: Time period:
$\frac{T'}{T_0} = \sqrt9 = 3$, so $T' = 3T_0$.

Final Answer:
The period becomes 3 T0, option (C). \[ \boxed{3T_0} \]