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Q.

A thin uniform rod of negligible mass and length l is attached to the floor by a frictionless hinge as shown. A horizontal spring with force constant k connects the other end of the rod to a vertical wall. The rod is in a uniform magnetic field B directed into the plane of the figure. There is a current i in the rod as shown and at equilibrium rod makes 53° angle with the floor. The energy stored by the spring in equilibrium is

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a

516i2B2l2k

b

33128i2B2l2k

c

25128i2B2l2k

d

716i2B2l2k

answer is C.

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Detailed Solution

Balancing torque about hingeiBl22=kxlsin53°​⇒x=58iBlk \ Energy stored  =12kx2=25128i2B2l2k
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