Question

The distance between the centres of moon and earth is D. The mass of earth is 81 times the mass of moon . At what distance from the centre of the earth, the gravitational force will be 0

Answer 1

as much we go deep of the earth the gravity will be that much less so centre of earth is always be0

Answer 2

The point where the force is zero must also be zero from moon's gravitaional force.

               Force at that point due to earth = Force due to moon

               $\frac {GM} {x^2} = \frac {Gm} {(R- x)^2}$

M = 81m

               $\frac {81m} {x^2} = \frac {m} {(R- x)^2}$

               $81 (R - x)^2 = x^2$

               $9(R - x)^2 = x$

               9R = 10x

               $x = 0.9R = 0.9 \times 4 \times 10^8 = 3.6\times 10^8 m$