A short bar magnet having magnetic moment 4 Am 2, placed in a vibrating magnetometer, vibrates with a time period of 8 s. Another short bar magnet having a magnetic moment 8 Am 2 vibrates with a time period of 6 s. If the moment of inertia of the second magnet is 9 × 10-2 kg - m 2, the moment of inertia of the first magnet is (assume that both magnets are kept in the same uniform magnetic induction field.)

Question

A short bar magnet having magnetic moment 4 Am 2, placed in a vibrating magnetometer, vibrates with a time period of 8 s. Another short bar magnet having a magnetic moment 8 Am 2 vibrates with a time period of 6 s. If the moment of inertia of the second magnet is 9 × 10-2 kg - m 2, the moment of inertia of the first magnet is (assume that both magnets are kept in the same uniform magnetic induction field.) (A) 9 × 10-2 kg - m 2 (B) 8 × 10-2 kg - m 2 (C) 5.33 × 10-2 kg - m 2 (D) 12.2 × 10-2 kg - m 2

Tardigrade Admin · Accepted Answer

We know that the time period of a vibrating bar magnet

T = 2 π \frac{I}{M B _{H}}

Given,

T_{1} = 8 s, I_{1} = I, M = 4 A m^{2}

8 = 2 π \frac{1}{4 \times B _{H}}

...(i)
Given,

T_{2} = 6 s, I_{2} = 9 \times 1 0^{- 2} k g - m^{2}, M = 8 A m^{2}

6 = 2 π \frac{9 \times 1 0 ^{- 2}}{8 \times B _{H}}

...(ii)
Dividing Eqs. (i) and (ii)

\frac{8}{6} = \frac{2 I}{9 \times 1 0 ^{- 2}}

Squaring both sides and solving, we have

I = 8 \times 1 0^{- 2} k g - m^{2}

$9 \times 1 0^{- 2} k g - m^{2}$

$8 \times 1 0^{- 2} k g - m^{2}$

$5.33 \times 1 0^{- 2} k g - m^{2}$

$12.2 \times 1 0^{- 2} k g - m^{2}$

9×10−2kg−m2

8×10−2kg−m2

5.33×10−2kg−m2

12.2×10−2kg−m2

$9 \times 1 0^{- 2} k g - m^{2}$

$8 \times 1 0^{- 2} k g - m^{2}$

$5.33 \times 1 0^{- 2} k g - m^{2}$

$12.2 \times 1 0^{- 2} k g - m^{2}$