Radius of moon is 1/4 times that of earth and mass is 1/81 times that of earth. The point at which gravitational field times that of earth. The point at which gravitational field due to earth becomes equal and opposite to that of moon, is x R from centre of earth. Find the value of x, (Distance between centres of earth and moon is 60R, where R is radius of earth)

Explanation

To solve the problem, we need to find the point where the gravitational field due to the Earth becomes equal and opposite to that of the Moon.

### Given:
- Radius of the Moon, \( R_m = \frac{1}{4} R_e \) (where \( R_e \) is the radius of the Earth)
- Mass of the Moon, \( M_m = \frac{1}{81} M_e \) (where \( M_e \) is the mass of the Earth)
- Distance between the centers of the Earth and the Moon, \( D = 60R_e \)

### Step-by-Step Solution:
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