Distance between the raeth and the moon is 4*10^5 km. Mass of earth is 81 times the mass of the moon.Calculate the position of the point on the line joining the centres of the earth and the moon where gravitational field is zero.

let x is the distance from the  earth where the gravitational force is zero.M is the mass of the earthm is the mass of the moon.ler R be the distance between them.force at that point due to earth = force at that point due to moonGMx2 = Gm(R-x)2M = 81 m81mx2 = m(R-x)281(R-x)2 = x29(R-x) = x9R -9x = x9R = 10xx = 0.9Rx = 0.9×4×108 = 3.6×108 m

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