Given that acceleration due to gravity varies inversely as the square of the distance from the center of earth, find its value at a height of 64 km from the earth's surface , if the value at the surface be `9.81ms^(-2)`. Radis of earth`=6400km`.

Explanation

To find the acceleration due to gravity at a height of 64 km from the Earth's surface, we can follow these steps:

### Step 1: Understand the relationship between gravity and distance
The acceleration due to gravity (g) varies inversely with the square of the distance (r) from the center of the Earth. This can be expressed mathematically as:
\[ g \propto \frac{1}{r^2} \]
or
\[ g = \frac{k}{r^2} \]
where k is a constant.
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