The acceleration due to gravity at a depth of 1600 km inside the earth.

Options

A. 0
B. 9.8 `m//s^2`
C. 7 `m//s^2`
D. 7.35 `m//s^2`

Answer

To find the acceleration due to gravity at a depth of 1600 km inside the Earth, we can use the formula:

\[ g' = g \left( 1 - \frac{d}{R} \right) \]

where:
- \( g' \) is the acceleration due to gravity at depth,
- \( g \) is the acceleration due to gravity at the surface (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( d \) is the depth (1600 km),
- \( R \) is the radius of the Earth (approximately \( 6400 \, \text{km} \)).

### Step-by-step Solution:

1. **Identify the values**:
- Surface gravity, \( g = 9.81 \, \text{m/s}^2 \)
- Depth, \( d = 1600 \, \text{km} \)
- Radius of the Earth, \( R = 6400 \, \text{km} \)

2. **Substitute the values into the formula**:
\[ g' = 9.81 \left( 1 - \frac{1600}{6400} \right) \]

3. **Calculate the fraction**:
\[ \frac{1600}{6400} = \frac{1}{4} = 0.25 \]

4. **Substitute back into the equation**:
\[ g' = 9.81 \left( 1 - 0.25 \right) \]

5. **Simplify the expression**:
\[ g' = 9.81 \times 0.75 \]

6. **Calculate the final value**:
\[ g' = 9.81 \times 0.75 = 7.3575 \, \text{m/s}^2 \]

7. **Round the result**:
\[ g' \approx 7.35 \, \text{m/s}^2 \]

### Final Answer:
The acceleration due to gravity at a depth of 1600 km inside the Earth is approximately \( 7.35 \, \text{m/s}^2 \).

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