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Question

A point mass m is released from rest at a distance of 3R from the centre of a thin walled hollow sphere of radius R and mass M as shown. The hollow sphere is fixed in position and the only force on the point mass is the gravitational attraction of the hollow sphere. There is a very small hole in the hollow sphere through which the point mass falls as shown. The velocity of point mass when it passes through point P at a distance R/2 from centre of sphere, is

  1. square root of fraction numerator 2 G M over denominator 3 R end fraction end root    
  2. square root of fraction numerator 5 G M over denominator 3 R end fraction end root    
  3. square root of fraction numerator 25 G M over denominator 24 R end fraction end root    
  4. None of these    

The correct answer is: None of these


    Inside spherical shell V is constant, so from energy convocation
    negative fraction numerator G M m over denominator 3 R end fraction equals fraction numerator m v to the power of 2 end exponent over denominator 2 end fraction minus fraction numerator G M m over denominator R end fraction
    Is v equals square root of fraction numerator 4 G M over denominator 3 R end fraction end root

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