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Question

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 space displasded from its equilibrium position and left then it executes SHM. The period of oscillation will be

A
2π ((Rr)1.4g)
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B
2π(Rrg)
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C
2π(rRa)
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D
2π(Rgr)
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Solution

The correct option is B 2π(Rrg)
After displacing the sphere, it will experience force towards the mean position which will be provided by component of gravitaional force
From the figure we can write θ=xR
Tangential acceleration,
at=g sinθ=gθ
at=gx(Rr)
Motion is SHM, with time period
T=2πDisplacementAcceleration
2π  xgx(Rr)
2πRrg
Final answer: (b)


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