MHT CET20227 Aug 2022Evening ShiftPhysicsOscillationsActual
A sphere of radius ' r ' is Kept on a concave minor of radius of curvature ' R ' The arrangement is kept on a horizontal table If the sphere is displaced from its equilibrium position and left then it executes S.H.M. The period of oscillation will be ( g = acceleration due to gravity.)
Options
- A2 [( R / gr )]^ 1 2
- B2 [( R - r ) / g ]^ 1 2
- C2 [( R - r ) 1.4 / g ]^ 1 2
- D2 [( Rr ) / g ]^ 1 2
Correct answer
B. 2 [( R - r ) / g ]^ 1 2
Step-by-step solution
Consider the figure below: Restoring torque about axis of rotation O is given by, aligned & =- mgr _ =- mg ( R - r ) & = m ( R - r )^2 & =- ( g ( R - r ) ) =- ^2 aligned The angular frequency can be written as: ^2= ( g R - r ) T = 2 =2 ( R - r ) g