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Question

A uniform rod of mass m and length l=1 m is hinged to a cart in vertical position as shown in figure. If cart starts moving at acceleration a=2 m/s2. EMF induced(in volts) across rod when it becomes horizontal, if uniform magnetic field of B = 2T exist in space is [g=10 m/s2]

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Solution


When the frame of reference is connected to the truck, there will be a pseudo force of ma acting on the rod at the centre, in the backward direction.
Work done by the pesudo torque and the weight as the rod rotates by dθ is,
dW=π20mal2cosθdθ+mgl2sinθdθ=mgL2+maL2

By work energy theorem,
mgL2+maL2=12Iω2
ω2=3(g+a)L
ε=BωL22=B2L23(g+a)L=36
ε=6.708 V

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