A sphere of radius r is kept on a concave mirror of radius of curvature R . arrangement is kept on a

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13.Oscillations

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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

A

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

B

$2\pi \sqrt {\left( {\frac{{R - r}}{g}} \right)} $

C

$2\pi \sqrt {\left( {\frac{{rR}}{a}} \right)} $

D

$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}} $

Standard 11

Physics

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