Two point masses m and 4m are separated by an unknown distance r . The gravitational potential at the point on the line joining them where the net gravitational field is zero, is found to be -V₀ . The separation distance r between the two masses is:

Step-by-step solution

Let the neutral point (where the net gravitational field is zero) be at a distance x from the mass m . Equating the magnitudes of the gravitational fields produced by both masses at this point: Gm x^2 = G(4m) (r-x)^2 Taking the square root on both sides: 1 x = 2 r-x r - x = 2x x = r 3 The distance of this neutral point from the mass 4m is r - r 3 = 2r 3 . The net gravitational potential V at this point is the scalar sum of the potentials due to both masses: V = - Gm x - G(4m) r-x V = - Gm ( r 3 ) - 4Gm ( 2r 3 ) V =