A stepped dies of mass `M` and radius `R` is pivoted at its center `C` smoothly. An inextensible string connected with a light spring of stiffness `k` passes over the pulley. One end of the string is rigidly connected with the ground and the other end is attached to a body of mass `m` . If the string does not slide on the pulley, find the angularfrequency of oscillation of the syytem

Answer

`sqrt((2 kR^(2))/(MR^(2) + 2 mr^2)))`

Explanation

The net torque produced by the spring when the dise is rotated through an angle `theta` is
`tau_(C ) = (kx) R = (I_(C) + mr^(2)) alpha`
where `x = R theta and I_(C) = MR^(2)`
or `alpha = (kR^(2))/(((MR^(2))/(2) + mr^(3))) theta or omega = sqrt((2 kR^(2))/(MR^(2) + 2 mr^2))`