An acceleration of moon with respect to earth is 0.0027 `ms^-2` and the acceleration of an apple falling on earth's surface is about `10ms^-2`. Assume that the radius of the moon is one fourth of the earth's radius. If the moon is stopped for an instant and then released, it will fall towards the earth. The initial acceleration of the moon toward the will be

Options

A. `10ms^-2`
B. `0.0027ms^-2`
C. `6.4ms^-2`
D. `5.0ms^-2`

Answer

To find the initial acceleration of the moon towards the Earth when it is stopped for an instant and then released, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Data**:
- Acceleration of the moon with respect to Earth: \( a_{me} = 0.0027 \, \text{m/s}^2 \)
- Acceleration of an apple falling on Earth's surface: \( g = 10 \, \text{m/s}^2 \)
- Radius of the moon is one-fourth of the radius of the Earth: \( R_m = \frac{1}{4} R_e \)

2. **Identify the Forces**:
- When the moon is in orbit, it experiences a centripetal force due to the gravitational attraction from the Earth. This force is balanced by the centrifugal force due to its circular motion.
- When the moon is stopped, the gravitational force from the Earth still acts on it, but the centrifugal force is absent.

3. **Calculate the Initial Acceleration**:
- The initial acceleration of the moon towards the Earth when it is released can be considered as the gravitational acceleration acting on it. This is the same as the acceleration of the moon with respect to the Earth when it is in orbit, which is given as \( 0.0027 \, \text{m/s}^2 \).

4. **Conclusion**:
- Therefore, the initial acceleration of the moon towards the Earth when it is released is \( 0.0027 \, \text{m/s}^2 \).

### Final Answer:
The initial acceleration of the moon towards the Earth will be \( 0.0027 \, \text{m/s}^2 \).

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