Question

If the mass of moon is $M/81$ where $M$ is the mass of earth, find the distance of the point from the moon, where gravitational field due to earth and moon cancel each other. Given that distance between earth and moon is $60R$ where $R$ is the radius of earth.

• A. $4R$
• B. $8R$
• C. $2R$
• D. $6R$

Answer 1

Answer: (D)

$6R$

Let at a distance x from the earth, field equalizes each, other. So, applying Newton's law of gravitation
$\frac{GM}{x^2}=\frac{GM/81}{(60R-x{)}^2}$

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

$\Rightarrow \frac{1}{x}=\frac{1}{9(60R-x)}$
$x=540R-9x\Rightarrow 10x=540R$
$x=54R$;
Distance of the point from moon $=60R-54R=6R$