Question

ANSWER WITH EXPLANATION TO GET 19 POINTS :-)
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 = 60 R, Radius of Earth=R, Mass of Earth = M
(A) 2 R (B) 6 R (C) 4 R (D)8 R

Answer 1

Answer:

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

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

Gravitational force on the mass due to Earth

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

Gravitational force on the mass due to Moon

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.