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 posit

Question

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.)

TestHub · Accepted Answer

Consider the figure below: Restoring torque about axis of rotation O is given by, ​ τ = − mgr ⊥ ​ = − mg ( R − r ) sin θ = m ( R − r ) 2 α ⇒ α = − ( ( R − r ) g ​ ) θ = − ω 2 θ ​ The angular frequency can be written as: ω 2 = ( R − r g ​ ) ∴ T = ω 2 π ​ = 2 π g ( R − r ) ​ ​

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