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  4. A bar magnet is oscillating in the earth's magnetic field with time period T. If its mass is increased four times, then its time period will be

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

J & K CETJ & K CET 2004

Solution:

The time period of vibration magnetometer is given by
$T=2 \pi \sqrt{\frac{I}{M H}}$
where $I$ is moment of inertia, $M$ the magnetic moment
and $H$ the horizontal component of earth's magnetic field.
Also, $I =m r^{2}$ where $m$ is mass and $r$ the radius.
When mass is increased four times. $I'=4 I$
$\therefore T'=2 \pi \sqrt{\frac{4 I}{M H}}$
$=2 \times 2 \pi \sqrt{\frac{I}{M H}}=2\, T$