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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
$2\pi \sqrt {\left( {\frac{{\left( {R - r} \right)1.4}}{g}} \right)} $
$2\pi \sqrt {\left( {\frac{{R - r}}{g}} \right)} $
$2\pi \sqrt {\left( {\frac{{rR}}{a}} \right)} $
$2\pi \sqrt {\left( {\frac{R}{{gr}}} \right)} $
Solution

(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
$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}} $