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A conducting wire of length I and mass m is placed on two inclined rails as shown in figure. A current i is flowing in the wire in the direction shown. When no magnetic field is present in the region, the wire is just on the verge of sliding. When a vertically upward magnetic field is switched on, the wire starts moving up the incline. The distance travelled by the wire as a function of time r will be

a
12IBlm-2gt2
b
12IBlm×1cosθ-2g sinθt2
c
12IBlm-2g sinθt2
d
12IBlmcos 2θcosθ-2g sinθt2

detailed solution

Correct option is D

The front view of the arrangement is shown in figure.From initial condition, mg sinθ = μ mg cosθ⇒μ=tanθma=IBlcosθ-mgsinθ-μNN=mg cosθ+IBl sinθ⇒a=IBlmcosθ-2g sinθ-IBlmsin2θcosθ=IBlmcos 2θcos θ-2g sinθNow, s=12at2=12IBlmcos 2θcos θ-2g sinθt2

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