AP EAMCET2013PhysicsMagnetic Properties of Matter
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.)
Options
- A9 10⁻² ~kg - m ^2
- B8 10⁻² ~kg - m ^2
- C5.33 10⁻² ~kg - m ^2
- D12.2 10⁻² ~kg - m ^2
Correct answer
B. 8 10⁻² ~kg - m ^2
Step-by-step solution
We know that the time period of a vibrating bar magnet T=2 I M B_H Given, T₁=8 ~s , l₁=I, M=4 Am ^2 8=2 1 4 B_H Given, T₂=6 ~s , I₂=9 10⁻² ~kg - m ^ 2 , M=8 Am ^2 6=2 9 10⁻² 8 B_H Dividing Eqs. (i) and (ii) 8 6 = 2 l 9 10⁻² Squaring both sides and solving, we have I=8 10⁻² ~kg - m ^ 2