Two bodies of masses m and 4m are placed at a distance r. Calculate the gravitational potential at a point on the joining them where the gravitational field is zero.

Two bodies of masses m and 4m are placed at a distance r. Calculate th

1.	Two bodies of masses m and 4m are placed at a distance r. Calculate the gravitational potential at a point on the joining them where the gravitational field is zero.
Answer» Solution :Let Thepoint be the position when the gravitational FIELDIS zero . ` (Gm)/(x^(2)) = (G(4M))/((r-x)^(2))` ` 1/(x^(2)) = 4/((r-x)^(2))` Square root on the sides ,`1/x = 2/((r-x)) ` ` x = r/3 ` The POINTP is distance`r/3` from mass .m. and`(2R)/3` frommass .4m. Gavitational potential` V = (-Gm)/((r/3))- (G(4m))/(((2r)/3))` ` = (-3(Gm))/4 - (3G(4m))/(2r)= (-3Gm)/r - (12Gm)/(2r) rArr V = (-9Gm)/r `