A rocket is fired the Earth towards the Moon. At what distance from the Moon is the gravitational force on the rocket is zero. Mass of Earth is `6 xx 10^(24) kg` , mass of moon is ` 7.4xx 10^(22) kg` and distance between moon and earth is `3.8xx 10^(8)m`. Neglect the effect of the sun and other planes.

Explanation

To solve the problem, we need to find the distance from the Moon at which the gravitational force acting on the rocket is zero. We will denote the distance from the Earth to the rocket as \( R - x \) and the distance from the Moon to the rocket as \( x \).

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of the Earth, \( M_E = 6 \times 10^{24} \, \text{kg} \)
- Mass of the Moon, \( M_M = 7.4 \times 10^{22} \, \text{kg} \)
- Distance between the Earth and the Moon, \( R = 3.8 \times 10^{8} \, \text{m} \)
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