Physics-
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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 sphere is displaced from its equilibrium position and left, then it executes S.H.M. The period of oscillation will be

  1. 2 pi square root of open parentheses fraction numerator open parentheses R minus r close parentheses 1.4 over denominator g end fraction close parentheses end root    
  2. 2 pi square root of open parentheses fraction numerator R minus r over denominator g end fraction close parentheses end root    
  3. 2 pi square root of open parentheses fraction numerator r R over denominator a end fraction close parentheses end root    
  4. 2 pi square root of open parentheses fraction numerator R over denominator g r end fraction close parentheses end root    

The correct answer is: 2 pi square root of open parentheses fraction numerator R minus r over denominator g end fraction close parentheses end root


    Tangential acceleration, a subscript t end subscript equals negative g sin invisible function application theta equals negative g theta
    a subscript t end subscript equals negative g fraction numerator x over denominator left parenthesis R minus r right parenthesis end fraction

    Motion is S.H.M., with time period
    T equals 2 pi square root of fraction numerator text displacement end text over denominator text acceleration end text end fraction end root equals 2 pi square root of fraction numerator x over denominator fraction numerator g x over denominator left parenthesis R minus t right parenthesis end fraction end fraction end root equals 2 pi square root of fraction numerator R minus r over denominator g end fraction end root

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