A metal rod of length 'L' and maws 'm' is pivoted at one end A thin disc of mass 'M' and radius 'R' (

A metal rod of length 'L' and maws 'm' is pivoted at one end A thin di

1.	A metal rod of length 'L' and maws 'm' is pivoted at one end A thin disc of mass 'M' and radius 'R' (
Answer» Restoring torque in case A = Restoring torque in case B Restorings torque in case A lt Restoring torque in case B Angular frequency for case A gt Angular frequency for case B. Angular frquency for case A lt Angular frequency for case B. SOLUTION :The fact that disc is free to rotate or not does not affect the forces ACTING on the system and hence restoring torque remains same in both the casesso option (a) is correct. In case A disc is not free to rotate about itscentre hence it has to change its orientation during the oscillation and its moment of inertia as a disc will be counted. But in second case disc will oscillate without changing its orientation andit will be just like a POINT mass attached at theend of rod. We can understand that moment of inertia in case A will be more than in case B. Frequency is INVERSELY proportional to square root of moment of inertia, hence we can understand that option (d) is ALSO correct.