Find the distance of a point from the earth's centre where the resultant gravitational field due to the earth and the moon is zero The mass of the earth is `6.0 xx 10^(24)kg` and that of the moon is `7.4 xx 10^(22)kg` The distance between the earth and the moon is `4.0 xx 10^(5)km` .

Explanation

To find the distance of a point from the Earth's center where the resultant gravitational field due to the Earth and the Moon is zero, we can follow these steps:

### Step 1: Define the Variables
Let:
- \( M_e = 6.0 \times 10^{24} \, \text{kg} \) (mass of the Earth)
- \( M_m = 7.4 \times 10^{22} \, \text{kg} \) (mass of the Moon)
- \( d = 4.0 \times 10^{5} \, \text{km} = 4.0 \times 10^{8} \, \text{m} \) (distance between the Earth and the Moon)
- \( x \) = distance from the center of the Earth to the point where the gravitational fields cancel out.
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