Shows a situation similar to the previous problem. All parameters are the same except that a battery of emf `epsilon` and a variable resistance R are connected wires. Let `theta` be the angle made by the rod from the horizontal position (shown in the figurer), measuredin the clockwise direction. During the part of the motion `Oltthetaltpi/4` the only forces acting on the rod are gravity and the forces exerted by the magnetic field and the pivot. However, during the part of the motion, the resistance R is varied in such a way that the rod continues to rotate with a constant angular velocity `omega`. Find the value of R in terms of the given quantities.

Explanation

E.m.f=(B omega a^2)/2 [from previous problem] `
Current=(e+E)/R=(B omega a^2 +E)/(2R)`
`=(B omega a^2+2E)/(2R) `
` mg cos theta= ilB`
`[Net force acting on the rod is 0)`
`mg cos theta =(B omega a^2+2E)/(2R) (axxB)`
` R=(B omega a^2+2E)aB/(2mg cos theta)`.