Question

The mass of the earth is $81$ times the mass of the Moon and the distance between the earth and the Moon is $60$ times the radius of the earth. If $R$ is the radius of the earth, then the distance between the Moon and the point on the line joining the Moon and the earth where the gravitational force becomes zero is

• A. $30R$
• B. $15R$
• C. $6R$
• D. $5R$

Answer 1

Answer: (C)

$6R$

Let the mass of moon be M. Then the mass of earth is 81 M.

Let x be the distance from moon where the gravitational force on a body of mass 'm' is zero.

At that point, gravitational force of earth=gravitational force of moon

$⟹\frac{G\left(81M\right)m}{(60R-x{)}^2}=\frac{GMm}{x^2}$

$⟹x=6R$.

Where $R$ is radius of the earth