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Question

Two concentric shells of uniform density of mass M1 and M2 are situated as shown in the figure. The forces experienced by a particle of mass m when placed at positions A, B and C respectively are (given OA = p, OB = q and OC = r)

  1. z e r o comma blank G fraction numerator M subscript 1 end subscript m over denominator q to the power of 2 end exponent end fraction blank a n d blank G fraction numerator open parentheses M subscript 1 end subscript plus M subscript 2 end subscript close parentheses m over denominator p to the power of 2 end exponent end fraction    
  2. G fraction numerator open parentheses M subscript 1 end subscript plus M subscript 2 end subscript close parentheses m over denominator p to the power of 2 end exponent end fraction comma G fraction numerator open parentheses M subscript 1 end subscript plus M subscript 2 end subscript close parentheses m over denominator q to the power of 2 end exponent end fraction blank a n d blank G fraction numerator M subscript 1 end subscript m over denominator r to the power of 2 end exponent end fraction    
  3. G fraction numerator M subscript 1 end subscript m over denominator q to the power of 2 end exponent end fraction comma G fraction numerator open parentheses M subscript 1 end subscript plus M subscript 2 end subscript close parentheses m over denominator p to the power of 2 end exponent end fraction blank a n d blank z e r o    
  4. G fraction numerator open parentheses M subscript 1 end subscript plus M subscript 2 end subscript close parentheses m over denominator p to the power of 2 end exponent end fraction comma G fraction numerator M subscript 1 end subscript m over denominator q to the power of 2 end exponent end fraction blank a n d blank z e r o    

The correct answer is: G fraction numerator open parentheses M subscript 1 end subscript plus M subscript 2 end subscript close parentheses m over denominator p to the power of 2 end exponent end fraction comma G fraction numerator M subscript 1 end subscript m over denominator q to the power of 2 end exponent end fraction blank a n d blank z e r o

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