A magnetic dipole of magnetic moment `6 xx 10^(-2)A m^(2)` and moment of inertia `12 xx 10^(-6) kg m^(2)` performs oscillations in a magnetic field of `2 xx 10^(-2)T`. The time taken by the dipole to complete 20 oscillations is (`pi = 3`)

Options

A. 36 s
B. 6 s
C. 12 s
D. 18 s

Answer

C

Explanation

Magnetic moment (M) `= 6xx10^(-2)A m^(2)`
Moment of inertia (I) `= 12xx10^(-6)kg m^(2)`
Magnetic field (B) `= 2xx10^(-2)T`
We know that,
Time (t) `= 2pi sqrt((I)/(MB))`
`= 2pi sqrt((12xx10^(-5))/(6xx10^(-2)xx2xx10^(-2)))`
`= 2pi sqrt((12xx10^(-2))/(12))`
`= 2pi x10^(-1)`
For 20 oscillation
Time (t) `= 20xx2pi xx10^(-1)=12s`