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Question

Two spheres each of mass M and radius R are separated by a distance of r. The gravitational potential at the midpoint of the line joining the centres of the spheres is

  1. negative fraction numerator G m over denominator r end fraction
  2. negative fraction numerator 2 G m over denominator r end fraction
  3. negative fraction numerator G M over denominator 2 r end fraction
  4. negative fraction numerator 4 G M over denominator r end fraction

The correct answer is: negative fraction numerator 4 G M over denominator r end fraction


    Let P is the midpoint of the line joining the centres of the spheres.
    The gravitational potential at point P is

    V subscript P equals negative fraction numerator G M over denominator r divided by 2 end fraction minus fraction numerator G M over denominator r divided by 2 end fraction equals negative fraction numerator 2 G M over denominator r end fraction minus fraction numerator 2 G M over denominator r end fraction equals negative fraction numerator 4 G M over denominator r end fraction

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