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Two bar magnets of same length and breadth having magnetic moments M and 4M respectively are joined with likes poles together and suspended in a uniform magnetic field B, it oscillates with time period T=3 s. If the polarity of one of the magnet is reversed and the combination is again made to oscillate in the same field. Find the new time period of this combination.

A
3 s
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B
5 s
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C
2 s
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D
2 s
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Solution

The correct option is B 5 s
Given:
M1=M; M2=4M; T1=3 s

In a combination, like poles placed together, so net dipole moment will be

Mres=M1+M2=M+4M=5M

And we know that, the time period of oscillation of bar magnet in uniform magnetic field is

T=2πIMB

So, for the combination of like poles,

T1=2πI(5M)B .......(1)

In a combination, unlike poles are together, resultant moment will be

Mres=|M1M2|=|M4M|=3M

So time period for this combination will be

T2=2πI(3M)B ........(2)

On dividing eq. (2) by (1), we get

T2T1=53

T2=53×T1=5 s

Hence, option (B) is correct.

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