A bar magnet of moment of inertia `9 xx 10 ^(-5) kg m ^(2)` placed in a vibration magnetometer and oscillating in a uniform magnetic field `16 pi ^(2) xx 10 ^(-5) ` T makes 20 oscillations in 15 s. The magnetic moment of the bar magnet is

Options

A. `3 A -m ^(2)`
B. `2 A- m ^(2)`
C. `5 A - m ^(2)`
D. `6 A- m ^(2)`

Explanation

Given,
`I = 9 xx 10 ^(-5) kg - m ^(2)`
`B = 16 pi ^(2) xx 10 ^(-5) T`
`T = (15)/(20) = 0.75`
The time period
`T = 2pi sqrt ((I)/(MB))`
`M = 4pi ^(2) xx (I)/( T ^(2)B)`
`= 4pi ^(2) xx 9 xx 10 ^(-5)/( 16pi ^(2) xx 10 ^(-5) xx (0.75) ^(2))`
`= (9)/(4xx 0.5625)`
`= (9.00)/(2.25) = 4 A-m^(2)`