A uniform solid disc of mass M and radius R rolls without slipping on a rough horizontal surface. Its centre is connected to a horizontal ideal spring of force constant k. What is the angular frequency of small oscillations?
Options

Question

A uniform solid disc of mass M and radius R rolls without slipping on a rough horizontal surface. Its centre is connected to a horizontal ideal spring of force constant k. What is the angular frequency of small oscillations?

Options

G1 Physics · Accepted Answer

For a rolling disc, I = MR²/2. The effective inertial mass for translation of the centre is Mₑ = M+I/R² = M+M/2 = 3M/2. Hence, ω² = k/(3M/2) = 2k/(3M). Therefore, ω = √[2k/(3M)]. Correct option: B.