Two heavy spheres of masses 2M and 8M are fixed at a distance L apart. What is the gravitational potential at a point on the line joining their centers where the net gravitational field is zero?

Step-by-step solution

Let the point of zero gravitational field be at a distance x from the mass 2M . Equating the magnitudes of the gravitational fields due to both masses at this point: G(2M) x^2 = G(8M) (L-x)^2 1 x^2 = 4 (L-x)^2 Taking the square root of both sides: 1 x = 2 L-x L - x = 2x x = L 3 The distance of the point from the mass 8M is L - x = 2L 3 . The gravitational potential at this point is the sum of the potentials due to both masses: V = - G(2M) x - G(8M) L-x V = - G(2M) L 3 - G(8M) 2L 3 V = - 6GM L - 12GM L = - 18GM L An