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A thin uniform rod with negligible mass ...

A thin uniform rod with negligible mass and length `l` is attached to the floor by a frictionless hinge at point `P`. A horizontal spring with force constant `k` connects the other end to wall. The rod is in a uniform magnetic field `B` directed into the plane of paper. What is extension in spring in equilibrium when a current is passed through the rod in direction shown? Assuming spring to be in natural length initially and it remains perpendicular to wall always.

A

`(5ilB)/(8k)`

B

`(3ilB)/(8k)`

C

`(5ilB)/(4k)`

D

`(5ilB)/(6k)`

Text Solution

Verified by Experts

The correct Answer is:
A
Magnetic force `F=Bil`
Net torque `P` is zero.

`F(1)/(2)=kxlsin53^(@)implies(Bil)/(2)=kx xx(4)/(5)`
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