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Infinite number of bodies, each of mass 2 ~kg are situated on x -axis at distance 1 ~m , 2 ~m , 4 ~m , 8 ~m , respectively from the origin. The resulting gravitational potential due to this system at the origin will be

Options

  1. A-G
  2. B- 8 3 G
  3. C- 4 3 G
  4. D-4 G

Correct answer

D. -4 G

Step-by-step solution

The resulting gravitational potential, array ll & V=-2 G [ 1 1 + 1 2 + 1 4 + 1 8 + ] & V=-2 G [1+ 1 2 + 1 2^2 + 1 2^3 ] & V=-2 G (1+ 1 2 )⁻¹ & V=- 2 G (1- 1 2 ) =- 2 G ( 1 2 ) =-4 G array

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