First slide

Magnetism

Question

A bar magnet of moment of inertia I is vibrated in a magnetic field of induction $0.4 \times 10^{- 4} T$ . The time period of vibration is 12sec. The magnetic moment of the magnet is $120 {Am}^{2}$ . The moment of Inertia of the magnet is ( in $K g m^{2}$ )

Moderate

A

$1750 \times 10^{- 2} {Kgm}^{2}$
B

$175 \times 10^{- 4} {Kgm}^{2}$
C

$2.1 π^{2} {Kgm}^{2}$
D

$1.5 \times 10^{- 2} {Kgm}^{2}$

Solution

Time period of Oscillation of Magnetic needle is
$T = 2 π \sqrt{\frac{I}{M B}} \Rightarrow T^{2} = 4 π^{2} \frac{I}{M B} \Rightarrow 4 π^{2} I = M B T^{2} \Rightarrow I = \frac{M B T^{2}}{4 π^{2}}$
Given data : T = 12 sec , $B = 4 \times 10^{- 5} T$ , $M = 120 A m^{2}$
$\begin{array}{l} ∴ I = \frac{120 \times 4 \times 10^{- 5} \times 144}{4 \times (3.14)^{2}} = 175 \times 10^{- 4} {Kgm}^{2} \end{array}$

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