Question

The point at which the gravitational force acting on any mass is zero due to the Earth and the Moon system is (The mass of the Earth is approximately $81$ times the mass of the Moon and the distance between the Earth and the Moon is $3,85,000km$.)

• A. 36,000 km from the Moon.
• B. 38,500 km from the Moon.
• C. 34500 km from the Moon.
• D. 30,000 km from the Moon.

Answer 1

Answer: (B)

38,500 km from the Moon.

For zero gravitational force acting on the mass $m_1$,
$\frac{GM{m}_1}{(d-x{)}^2}=\frac{Gm{m}_1}{x^2}$

Here $x$ is distance from moon, $M$ is mass of earth, $m$ is mass of moon and $d$ is the distance between the earth and moon.
$\Rightarrow \frac{M}{(d-x{)}^2}=\frac{m}{x^2}$

$\Rightarrow \frac{81m}{(d-x{)}^2}=\frac{m}{x^2}$

$\Rightarrow \frac{81}{(d-x{)}^2}=\frac{1}{x^2}$

$\Rightarrow \frac{(d-x{)}^2}{81}=x^2$

$\Rightarrow \frac{d-x}{9}=x$

Solving gives: $x=\frac{d}{10}=38,500$ km