Question

A bar magnet is oscillating in the earth's magnetic field with a time period $T$. If the mass is quadrupled, then its time period will be

• A. $T$
• B. $\frac{T}{2}$
• C. $4T$
• D. $2T$

Answer 1

The correct option is D $2T$

Time period

Time period (T) of oscillation of magnet,


$T=2\pi \sqrt{\frac{I}{MH}}$

$(I$ = moment of inertia of oscillating magnet, $M$= magnetic moment, $H$ = external magnetic field)

$I=m{k}^2$
(k=radius of gyration of magnet about axis of rotation, m= mass of magnet)

$\Rightarrow T=2\pi \sqrt{\frac{m{k}^2}{MH}}$

$\Rightarrow T\propto \sqrt{m}$

$\therefore \frac{T_1}{T_2}=\sqrt{\frac{m}{4m}}$

$\Rightarrow \frac{T_1}{T_2}=\frac{1}{2}$

$\Rightarrow T_2=2T_1$

Hence, the correct option is (C)