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Two bar magnets having same geometry wit...

Two bar magnets having same geometry with magnetic moments M and 2M, are firstly placed in such a way what their similar poles are same side then its time period of oscillation is `T_1`. Now the polarity of one of the magnet is reversed then time period of oscillation will be:-

A

`T_(1)ltT_(2)`

B

`T_(1)gtT_(2)`

C

`T_(1)=T_(2)`

D

`T_(1)=oo,T_(1)=0`

Text Solution

Verified by Experts

The correct Answer is:
A
Using the formula for time period for magnetic system
`" " T=2pi sqrt(((I)/(MH)))`
`" " Talpha (1)/(sqrtM)...........(i)`
When similar poles placed of a magnet is reversed, then
`" " m_(2)=2M-M=M`
So, from Eq. (i)
`" " T_(2) alpha (1)/(sqrt3M).......(ii) `
when the polarity of a magnet is reversed, then
` " " M_(2)=2M-M=M`
So, from Eq. (i)
`" " T_(2) alpha (1)/(sqrtM).......(iii) `
Now, dividing Eq. (iii) by Eq. (ii) by Eq. (iii), we get
`" " (T_(1))/(T_(2))=(sqrtM)/(sqrt3M)=(1)/(sqrt3)`
`Rightarrow" " T_(2)=sqrt3T_(1)`
`Hence" " T_(1)ltT_(2)`
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