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

Question

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 (A) 4T (B) 2T (C) T (D) r

Tardigrade Admin · Accepted Answer

The time period of vibration magnetometer is given by

T = 2 π \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

∴ T^{'} = 2 π \frac{4 I}{M H}

= 2 \times 2 π \frac{I}{M H} = 2 T

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

4T

2T

T

r

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