Question

At what distance from the centre of the moon is the point at which the strength of the field of earth's and moon's gravitational field is equal to zero.

Answer 1

The net gravitaional force due to both would be zero then after.

Hence

gravity Earth + gravity moon = 0

Gm/(x^2)+ GM/(D-x)^2 = 0

Aand given M = 81m

We get,

Gm/(x^2) + 81Gm/(D-x)^2

1/x = 9/(D-x)

9x = D-x

10x = D

x = D/10

10x = D

x = D/10