Question

A rod of mass m =2 kg and length l =3 m rotates about an axis passing through one end O and perpendicular to its length. The other end of rod A, slides without friction on a circular conducting rail (negligible resistance). A resistor R is connected to the rod and rail as shown. The whole set up lies in horizontal plane with uniform magnetic field B directed in to the plane of ring. The rod is given an angular speed ${\omega }_0$ and released. The total heat generated in the resistor R is 27 J. Find the value of ${\omega }_0$ in rad/s.___

Answer 1

$\frac{1}{2}{I}_0{\omega }^2$ =heat genertaed
$\frac{m{l}^2}{6}{\omega }_0^2=27{\omega }_0=3rad/s$