At what depth below the surface does the acceleration due to gravity becomes 70% of its value in the surface of earth ?

Answer

To find the depth below the surface of the Earth where the acceleration due to gravity becomes 70% of its value at the surface, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**:
We need to find the depth \( d \) at which the acceleration due to gravity \( G_d \) is 70% of the acceleration due to gravity at the surface \( G \). Mathematically, this can be expressed as:
\[ G_d = 0.7 G \]

2. **Use the Formula for Gravity at Depth**:
The formula for the acceleration due to gravity at a depth \( d \) below the surface is given by:
\[ G_d = G \left(1 - \frac{d}{R}\right) \]
where \( R \) is the radius of the Earth.

3. **Substitute the Known Values**:
We know that \( G_d = 0.7 G \). Therefore, we can set up the equation:
\[ 0.7 G = G \left(1 - \frac{d}{R}\right) \]

4. **Cancel \( G \) from Both Sides**:
Since \( G \) is not zero, we can divide both sides by \( G \):
\[ 0.7 = 1 - \frac{d}{R} \]

5. **Rearrange the Equation**:
Rearranging the equation gives:
\[ \frac{d}{R} = 1 - 0.7 = 0.3 \]

6. **Solve for Depth \( d \)**:
Now, multiply both sides by \( R \):
\[ d = 0.3 R \]

7. **Substitute the Radius of the Earth**:
The average radius of the Earth \( R \) is approximately \( 6400 \) km. Thus:
\[ d = 0.3 \times 6400 \text{ km} = 1920 \text{ km} \]

### Final Answer:
The depth below the surface where the acceleration due to gravity becomes 70% of its value at the surface of the Earth is **1920 km**.