A sphere of radius $r$ is kept on a concave mirror of radius of curvature $R$. The arrangement is kept on a horizontal table (the surface of concave mirror is frictionless and sliding not rolling). If the sphere is displaced from its equilibrium position and left, then it executes $S.H.M.$ The period of oscillation will be
Diffcult
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(b) Tangential acceleration, ${a_t} = - g\sin \theta = - g\theta $
${a_t} = - g\frac{x}{{(R - r)}}$
Motion is $S.H.M.$, with time period
${a_t} = - g\frac{x}{{(R - r)}}$
Motion is $S.H.M.$, with time period
$T = 2\pi \sqrt {\frac{{{\rm{displacement}}}}{{{\rm{acceleration}}}}} $
$ = 2\pi \sqrt {\frac{x}{{\frac{{gx}}{{(R - t)}}}}} = 2\pi \sqrt {\frac{{R - r}}{g}} $
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