If radius of earth shrinks by 1% then for acceleration due to gravity :

Options

A. No change at poles
B. No change at equator
C. Max. change at equator
D. Equal change at all locations

Answer

To solve the problem of how a 1% shrinkage in the radius of the Earth affects the acceleration due to gravity, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Formula for Acceleration due to Gravity**:
The acceleration due to gravity (g) at the surface of the Earth is given by the formula:
\[ g = \frac{GM}{R^2} \]
where \( G \) is the universal gravitational constant, \( M \) is the mass of the Earth, and \( R \) is the radius of the Earth.

2. **Identifying Changes**:
The problem states that the radius of the Earth shrinks by 1%. This means:
\[ \Delta R = -0.01R \]
where \( \Delta R \) is the change in radius.

3. **Using the Percentage Change Formula**:
To find the percentage change in acceleration due to gravity, we can use the formula for relative change:
\[ \frac{\Delta g}{g} \times 100 = \frac{\Delta M}{M} \times 100 + 2 \times \frac{\Delta R}{R} \times 100 \]
Here, we assume that the mass of the Earth (M) does not change, so \( \Delta M = 0 \).

4. **Substituting Values**:
Since \( \Delta M = 0 \), the first term becomes zero. The second term involves the change in radius:
\[ \frac{\Delta g}{g} \times 100 = 0 + 2 \times \frac{-0.01R}{R} \times 100 \]
Simplifying this gives:
\[ \frac{\Delta g}{g} \times 100 = 2 \times (-0.01) \times 100 = -2 \]

5. **Conclusion**:
This means that the acceleration due to gravity decreases by 2%. The reduction is uniform across the surface of the Earth, including at the poles and the equator.

### Final Answer:
The acceleration due to gravity decreases by 2% uniformly at all locations on the Earth's surface.

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