The height of any point P above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point P will be : (Given g= acceleration due to gravity at the surface of earth).

Options

A. `g//2`
B. `g//4`
C. `g//3`
D. `g//9`

Explanation

To solve the problem, we need to determine the acceleration due to gravity at a point P that is located at a height equal to the diameter of the Earth above the Earth's surface.

### Step-by-Step Solution:

1. **Identify the Variables:**
- Let the radius of the Earth be \( r \).
- The diameter of the Earth is \( 2r \).
- The height of point P above the Earth's surface is equal to the diameter of the Earth, which is \( 2r \).

2. **Calculate the Total Height of Point P from the Center of the Earth:**
- The total height of point P from the center of the Earth is the radius of the Earth plus the height above the surface:
\[ \text{Total height} = r + 2r = 3r \]

3. **Use the Formula for Acceleration Due to Gravity:**
- The formula for acceleration due to gravity at a distance \( h \) from the center of the Earth is given by:
\[ g' = \frac{GM}{r^2} \]
where \( G \) is the gravitational constant and \( M \) is the mass of the Earth.

4. **Substituting the Total Height into the Formula:**
- At point P, the distance from the center of the Earth is \( 3r \). Therefore, we substitute \( 3r \) into the formula:
\[ g' = \frac{GM}{(3r)^2} = \frac{GM}{9r^2} \]

5. **Relate it to the Acceleration Due to Gravity at the Surface:**
- The acceleration due to gravity at the surface of the Earth is:
\[ g = \frac{GM}{r^2} \]
- Thus, we can express \( g' \) in terms of \( g \):
\[ g' = \frac{g}{9} \]

6. **Conclusion:**
- Therefore, the value of acceleration due to gravity at point P is:
\[ g' = \frac{g}{9} \]

### Final Answer:
The value of acceleration due to gravity at point P is \( \frac{g}{9} \).

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