A bob of mass ' m ' is tied by a massless string whose other end is wound on a flywheel (disc) of radius ' R ' and mass ' m '. When released from the rest, the bob starts falling vertically downwards. If the bob has covered a vertical distance ' h ', then angular speed of wheel will be (There is no slipping between string and wheel, g - acceleration due to gravity)

Step-by-step solution

Conservation of mechanical energy is applied to the system, taking the initial state when the bob is at rest and the final state after it has fallen distance h . Initial potential energy is mgh , with zero kinetic energy for both bob and flywheel. Final energy consists of translational kinetic energy 1 2 mv^2 for the bob and rotational kinetic energy 1 2 I ^2 for the flywheel. For a solid disc, I = 1 2 mR^2 . The no-slip condition gives v = R . Equating initial and final energies: mgh = 1 2 m(R )^2 + 1 2 ( 1 2 mR^2