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Question

# A magnet is suspended in the magnetic meridian with an untwisted wire. The upper end of the wire is rotated through 180∘ to deflect the magnet by 30∘ from the magnetic meridian. When this magnet is replaced by another magnet, the upper end of the wire is rotated through 270∘ to deflect the magnet 30∘ from the magnetic meridian. The ratio of magnetic moments of magnets is

A
1:5
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B
1:8
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C
5:8
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D
8:5
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Solution

## The correct option is C 5:8Given, α1=180∘;α2=270∘θ1=30∘; θ2=30∘ Let M1 and M2 be the magnetic moments of magnets and H the horizontal components of earth's magnetic field. In equilibrium position, Torque in the wire=Restoring torque MBHsinθ=C(α−θ) ⇒ M1BHsinθ1=C(α1−θ1) ⇒ M1BHsin30∘=C(180∘−30∘) .....(1) Similarly, ⇒ M2BHsin30∘=C(270∘−30∘) .....(2) From (1) and (2) we get, ⇒ M1M2=150×(π180)240×(π180)=1524=58 ⇒M1:M2=5:8 <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (C) is the correct answer.

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