An infinite number of bodies, each of mass 2 kg, are situated on at distance 1m, 2m, 4m, 8m from the origin. What will be the resultant gravitational potential due to this system at the origin.

An infinite number of bodies, each of mass 2 kg, are situated on at di

1.	An infinite number of bodies, each of mass 2 kg, are situated on at distance 1m, 2m, 4m, 8m from the origin. What will be the resultant gravitational potential due to this system at the origin.
Answer» SOLUTION :Gravitationalpotentialat the origin is ` V = - G [ m/(r_(1)) +m/(r_(2)) +m/(r_(3)) +m/(r_(4)) + ...... ] = - G [ 2/1+2/5 +2/4 +2/8 +.......] ` ` - 2G [1+1/2 +1/(2^(2)) + 1/(3^(2))+ ......]= - 2G [ 1/(1-(1/2))] ` `V = - 4G`