Two bar magnet having same geometry with magnetic moment M and WM are placed in such a way that their similar poles are on the same side, then its time period of oscillation is `T_(1)`. Now, if the polarity of one of the magnet is reversed, then time period of oscillation is `T_(2)`, then

Options

A. `T_(1) lt T_(2)`
B. `T_(1) gt T_(2)`
C. `T_(1)=T_(2)`
D. `T_(2)=oo`

Answer

A

Explanation

The time period of bar magnet
`T=2pisqrt(I/(MH))`
where M=magnetic moment of magnet
I=moment of inertia
and H= horizontal component of magnetic field
when same poles of magnets are placed on same side, then net magnetic moment
`M_(1)=M+2M=3M`
`T_(1)=2pisqrt(1/(M_(1)H)) =2pisqrt(I/(3MH))`.....(i)
When opposite poles of magnets are placed on same side, then net magnetic moment
`M_(2)=2M-M=M`
`:. T_(2)=2pisqrt(1/(M_(2)H))=2pisqrt(1/(MH))....(ii)`
From eqs. (i) and (ii) we observe that
`T_(1) lt T_(2)`