Distance between the raeth and the moon is 4*10^5 km Mass of earth is 81 times the mass of - Physics - Gravitation

Question

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

Neha Gupta · Accepted Answer

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

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.