Acceleration due to gravity is minimum at

Options

A. The surface of earth
B. The depth 100 km from the earth`s surface
C. The centre of earth
D. The height 100 km from the earth`s surface

Answer

To determine where the acceleration due to gravity is minimum, we need to analyze how gravity behaves at different locations relative to the Earth.

### Step-by-Step Solution:

1. **Understanding Acceleration Due to Gravity (g)**:
The acceleration due to gravity at the surface of the Earth is approximately \( g = 9.8 \, \text{m/s}^2 \).

2. **Gravity at Depth**:
When moving below the Earth's surface, the acceleration due to gravity decreases. The formula for gravity at a depth \( d \) is given by:
\[ g' = g \left(1 - \frac{d}{R}\right) \]
where \( R \) is the radius of the Earth. As \( d \) approaches \( R \) (the center of the Earth), \( g' \) approaches zero.

3. **Gravity at the Center of the Earth**:
At the center of the Earth (where \( d = R \)), the acceleration due to gravity is:
\[ g' = g \left(1 - \frac{R}{R}\right) = g(1 - 1) = 0 \]
Thus, the acceleration due to gravity is zero at the center of the Earth.

4. **Gravity at Height**:
When moving above the Earth's surface, the acceleration due to gravity also decreases. The formula for gravity at a height \( h \) is:
\[ g' = g \left(1 - \frac{2h}{R}\right) \]
This value will be less than \( g \) but will not reach zero unless \( h \) is infinitely large.

5. **Comparing Values**:
- At the surface of the Earth, \( g = 9.8 \, \text{m/s}^2 \).
- At a depth of 100 km, \( g' \) is still positive but less than \( 9.8 \, \text{m/s}^2 \).
- At a height of 100 km, \( g' \) is also less than \( 9.8 \, \text{m/s}^2 \) but still positive.
- At the center of the Earth, \( g' = 0 \).

6. **Conclusion**:
The minimum value of acceleration due to gravity occurs at the center of the Earth, where \( g' = 0 \).

### Final Answer:
The acceleration due to gravity is minimum at the **center of the Earth**.