Find the point at which the gravitational force acting on any mass is zero due to the earth and the moon system. (such a point is called neutral point). The mass of the earth is 81 times the mass of the moon and the distance between the earth and the moon is 3,85,000km.

Explanation

To find the neutral point where the gravitational force acting on any mass is zero due to the Earth and Moon system, we can follow these steps:

### Step 1: Understand the Problem
We need to find a point (let's call it point P) along the line between the Earth and the Moon where the gravitational forces from both bodies balance each other out. The mass of the Earth (M_E) is 81 times the mass of the Moon (M_M), and the distance between the Earth and the Moon (R) is 385,000 km.

### Step 2: Set Up the Gravitational Force Equations
At point P, the gravitational force exerted by the Earth must equal the gravitational force exerted by the Moon on a mass m placed at point P.

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