Physics-
General
Easy

Question

A spherical hollow is made in a lead sphere of radius R such that its surface touches the outside surface of lead sphere and passes through the centre. What is the shift in the centre of lead sphere as a result of this hollowing?

  1. fraction numerator R over denominator 7 end fraction    
  2. fraction numerator R over denominator 14 end fraction    
  3. fraction numerator R over denominator 2 end fraction    
  4. R    

The correct answer is: fraction numerator R over denominator 14 end fraction


    Let centre of mass of lead sphere after hollowing be at point O subscript 2 end subscript comma where O O subscript 2 end subscript equals x
    Mass of spherical hollow m equals fraction numerator fraction numerator 4 over denominator 3 end fraction pi open parentheses fraction numerator R over denominator 2 end fraction close parentheses to the power of 2 end exponent M over denominator open parentheses fraction numerator 4 over denominator 2 end fraction pi R to the power of 3 end exponent close parentheses end fraction equals fraction numerator M over denominator 8 end fraction and
    x equals O O subscript 1 end subscript equals fraction numerator R over denominator 2 end fraction

    therefore blank x equals fraction numerator M cross times 0 minus open parentheses fraction numerator M over denominator 8 end fraction close parentheses cross times fraction numerator R over denominator 2 end fraction over denominator M minus fraction numerator M over denominator 8 end fraction end fraction equals fraction numerator fraction numerator M R over denominator 16 end fraction over denominator fraction numerator 7 M over denominator 8 end fraction end fraction equals negative fraction numerator R over denominator 14 end fraction
    therefore shift equals fraction numerator R over denominator 14 end fraction

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