With a standard rectangular bar magnet of length (l), breadth (b ; b

Question

With a standard rectangular bar magnet of length (l), breadth (b ; b< < l) and magnetic moment M, the time period of the magnet in a vibration magnetometer is 4 s. If the magnet is cut normal to its length into four equal pieces, the time period (in seconds) with one of the pieces is (A) 16 (B) 2 (C) 1 (D) 1 / 4

Tardigrade Admin · Accepted Answer

Time period of magnet in vibration magnetometer,

T = 2 π \frac{1}{M H}

where,

I =

moment of inertia of magnet

M =

magnetic moment

H =

horizontal component of earth's magnetic field

∴ \frac{T _{1}}{T _{2}} = \frac{I _{1}}{I _{2}} \cdot \frac{M _{2}}{M _{1}}

\Rightarrow \frac{4}{T _{2}} = \frac{m l ^{2} /12}{m /4 ( l /4 ) ^{2} /12}

= \frac{4 \times 16 \times 12}{12 \times 4} = 16

\Rightarrow \frac{4}{T _{2}} = 4

∴ T_{2} = 1 s

Q. With a standard rectangular bar magnet of length (l), breadth (b;b<<l) and magnetic moment M, the time period of the magnet in a vibration magnetometer is 4s. If the magnet is cut normal to its length into four equal pieces, the time period (in seconds) with one of the pieces is

16

2

1

1 / 4

Q. With a standard rectangular bar magnet of length $(l)$ , breadth $(b; b << l)$ and magnetic moment $M$ , the time period of the magnet in a vibration magnetometer is $4 s$ . If the magnet is cut normal to its length into four equal pieces, the time period (in seconds) with one of the pieces is