The time period of a thin bar magnet in earth's magnetic field is T. If the magnet is cut into four equal parts perpendicular to its length, the time period of each part in the same field will be

Question

The time period of a thin bar magnet in earth's magnetic field is T. If the magnet is cut into four equal parts perpendicular to its length, the time period of each part in the same field will be (A) T/2 (B) T/4 (C) √2 T (D) 2 T

Tardigrade Admin · Accepted Answer

Mass becomes 1 / 4 and length becomes 1 / 4. ∴ Moment of inertia I becomes, (1/4)((1/4))2=(1/64) therefore Magnetic moment M becomes 1 / 4 th. Now, as T=2 π √(1/M H), ∴ T becomes 1 / 4 th

Q. The time period of a thin bar magnet in earth's magnetic field is $T$ . If the magnet is cut into four equal parts perpendicular to its length, the time period of each part in the same field will be

T/2

T/4

$2 T$

2 T

Mass becomes $1/4$ and length becomes $1/4$ .
$∴$ Moment of inertia $I$ becomes, $\frac{1}{4} (\frac{1}{4})^{2} = \frac{1}{64}$ therefore Magnetic moment $M$ becomes $1/4$ th.
Now, as $T = 2 π \frac{1}{M H}$ ,
$∴ T$ becomes $1/4$ th

Q. The time period of a thin bar magnet in earth's magnetic field is T. If the magnet is cut into four equal parts perpendicular to its length, the time period of each part in the same field will be

T/2

T/4

2​T

2 T

Mass becomes 1/4 and length becomes 1/4. ∴ Moment of inertia I becomes, 41​(41​)2=641​ therefore Magnetic moment M becomes 1/4 th. Now, as T=2πMH1​​, ∴T becomes 1/4 th

Q. The time period of a thin bar magnet in earth's magnetic field is $T$ . If the magnet is cut into four equal parts perpendicular to its length, the time period of each part in the same field will be

$2 T$

Mass becomes $1/4$ and length becomes $1/4$ .
$∴$ Moment of inertia $I$ becomes, $\frac{1}{4} (\frac{1}{4})^{2} = \frac{1}{64}$ therefore Magnetic moment $M$ becomes $1/4$ th.
Now, as $T = 2 π \frac{1}{M H}$ ,
$∴ T$ becomes $1/4$ th