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Q.

A copper rod of mass m slides under gravity on two smooth parallel rails , with separation l and set at an angle of θ  with the horizontal. At the bottom, rails are joined by a resistance R. There is a uniform magnetic field B normal to the plane of the rails, as shown in the figure. The terminal speed of the copper rod is 

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a

mgRsinθB2l2

b

mgRcotθB2l2

c

mgRtanθB2l2

d

mgRcosθB2l2

answer is A.

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Detailed Solution

Copper rod will aquire terminal velocity when magnetic force = gravitational force 
Or  IlB=mgsinθ.
Also, I= induced emf R=BlvR
From equations (i) and (ii) we get 
B2l2vR=mgsinθ;v=mgRsinθB2l2

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