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 o

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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

TestHub · Accepted Answer

The resulting gravitational potential, ⇒ ⇒ ⇒ ​ V = − 2 G [ 1 1 ​ + 2 1 ​ + 4 1 ​ + 8 1 ​ + … ] V = − 2 G [ 1 + 2 1 ​ + 2 2 1 ​ + 2 3 1 ​ … ] V = − 2 G ( 1 + 2 1 ​ ) − 1 V = − ( 1 − 2 1 ​ ) 2 G ​ = − ( 2 1 ​ ) 2 G ​ = − 4 G ​

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