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Q.

A wire of cross-sectional area A forms three sides of a square and is free to rotate about axis OO1. If the structure is deflected by an angle θ from the vertical when current I is passed through it in a magnetic field B acting vertically upward and density of the wire is ρ, then the value of θ is given by

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a

2AρgiB=cotθ

b

2AρgiB=tanθ

c

AρgiB=sinθ

d

Aρg2iB=cosθ

answer is A.

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Detailed Solution

Let a is the side of square. Torque of current =MBsin(90-θ) =MBcosθ=ia2Bcosθ  Mass of each side =m=ρAa  Torque of gravity =2mga2sinθ+mgasinθ =2mgasinθ=2ρAga2sinθ Now, both torques should be same  i.e.,   ia2Bcosθ=2ρAga2sinθ ⇒  cotθ=2ρAgiB
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