A bar-magnet of moment of inertia 49 × 10-2 kg - m 2 vibrates in a magnetic field of induction 0.5 × 10-4 T. The time period of vibration is 8.8 s. The magnetic moment of the bar magnet is

Question

A bar-magnet of moment of inertia 49 × 10-2 kg - m 2 vibrates in a magnetic field of induction 0.5 × 10-4 T. The time period of vibration is 8.8 s. The magnetic moment of the bar magnet is (A) 350 A - m 2 (B) 490 A - m 2 (C) 3300 A - m 2 (D) 5000 A - m 2

Tardigrade Admin · Accepted Answer

Time period of magnet is T=2 π √(I/M H) or M= (4 π2 I/T2 H) or M=(4 ×(3.14)2 × 49 × 10-2/(8.8)2 × 0.5 × 10-4) or M=5000 A - m 2

Q. A bar-magnet of moment of inertia $49 \times 1 0^{- 2} k g - m^{2}$ vibrates in a magnetic field of induction $0.5 \times 1 0^{- 4} T$ . The time period of vibration is $8.8 s$ . The magnetic moment of the bar magnet is

$350 A - m^{2}$

$490 A - m^{2}$

$3300 A - m^{2}$

$5000 A - m^{2}$

Time period of magnet is
$T = 2 π \frac{I}{M H}$
or $M = \frac{4 π ^{2} I}{T ^{2} H}$
or $M = \frac{4 \times ( 3.14 ) ^{2} \times 49 \times 1 0 ^{- 2}}{( 8.8 ) ^{2} \times 0.5 \times 1 0 ^{- 4}}$
or $M = 5000 A - m^{2}$

Q. A bar-magnet of moment of inertia 49×10−2kg−m2 vibrates in a magnetic field of induction 0.5×10−4T. The time period of vibration is 8.8s. The magnetic moment of the bar magnet is

350A−m2

490A−m2

3300A−m2

5000A−m2