A conducting rod of length l  is hinged at point O. It is free to rotate in a vertical plane. There exists a uniform magnetic field B→  in horizontal direction. The rod is released from the horizontal position as shown. The potential difference between the ends of the rod when it has turned by θ (as shown in figure) is proportional to

The induced electro motive force Δv across ends of rotating rod about one end in magnetic field =B2l2ω .ω can be calculated according to law of conservation energy.Increase in rotational kinetic energy = decrease in gravitational potential energy  12Iω2=mgh⇒12ml23ω2=mg.l2sinθ⇒ω=3glsinθNow    ΔV=12Bl23glsinθ ……( 1 )∴ΔV∝sinθAlso from ( 1 ),  ΔV∝l32Therefore, the correct answer is ( D )