Question

Knowing that mass of the moon is M/81, find distance of a point from moon where gravitational field due
to earth and moon cancel each other. Given that distance between earth and moon = 60R, Radius of
Earth=R, Mass of Earth=M​

Answer 1

Answer:

The distance of the point from the moon is 6R

Explanation:

Let there be a mass m where the gravitational field of moon and earth cancel each other

Let the distance of the mass from moon be x

Then

Gravitational force on the mass due to Earth

$F=\frac{GMm}{(60R-x)^2}$

Gravitational force on the mass due to Moon

$F'=\frac{G(M/81)\times m}{x^2}$

F = F'

Thus

$\frac{GMm}{(60R-x)^2}=\frac{G(M/81)\times m}{x^2}$

$\implies \frac{1}{(60R-x)^2}=\frac{1}{81\times x^2}$

$\implies 81\times x^2=(60R-x)^2$

Taking square root on both sides

$9x=60R-x$

$\implies 10x=60R$

$\implies x=6R$

Therefore, the distance of the point from the moon is 6R

Hope this helps.