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.

Explanation

Let The point be the position when the gravitational field is 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 point P is distance `r/3` from mass .m. and `(2r)/3` from mass .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 `