Physics-
General
Easy

Question

A frictionless wire A B is fixed on a sphere of radius R. A very small spherical ball slips on this wire. The time taken by this ball to slip from A to B is

  1. fraction numerator 2 square root of g R end root over denominator g cos invisible function application theta end fraction    
  2. 2 square root of g R end root. fraction numerator cos invisible function application theta over denominator g end fraction    
  3. 2 square root of fraction numerator R over denominator g end fraction end root    
  4. fraction numerator g R over denominator square root of g cos invisible function application theta end root end fraction    

The correct answer is: 2 square root of fraction numerator R over denominator g end fraction end root


    Acceleration of the body along A B is g cos invisible function application theta
    Distance travelled in time t sec invisible function application equals A B equals fraction numerator 1 over denominator 2 end fraction open parentheses g blank c o s blank theta close parentheses t to the power of 2 end exponent
    From increment blank A B C comma blank A B equals 2 R cos invisible function application theta semicolon 2 R cos invisible function application theta equals fraction numerator 1 over denominator 2 end fraction g cos invisible function application theta t to the power of 2 end exponent
    rightwards double arrow t to the power of 2 end exponent equals fraction numerator 4 R over denominator g end fraction or t equals 2 square root of fraction numerator R over denominator g end fraction end root

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