Question

The distance of the centres of moon and earth is \( D \). The mass of earth is 81 times the mass of the moon. At what distance from the centre of the earth, the gravitational force will be zero?

• A. \( \frac{D}{2} \)
• B. \( \frac{2D}{3} \)
• C. \( \frac{4D}{3} \)
• D. \( \frac{9D}{10} \)

Hint:

For the gravitational force to be zero, the magnitudes of the forces from both bodies must be equal.

Answer 1

The Correct Option is C

Step 1: Gravitational Force at Zero.
At the point where the gravitational force between the moon and the earth is zero, the forces due to both bodies must be equal in magnitude and opposite in direction.

Step 2: Gravitational force equations.
Let the distance from the centre of the earth be \( r \). Then, using the inverse square law of gravitation, we can express the force due to the earth and moon at distance \( r \) and \( D - r \).

Step 3: Solving the equation.
After solving for \( r \), we find that the distance at which the gravitational force is zero is \( \frac{4D}{3} \).