At what altitude, the acceleration due to gravity reduces to half of its value as that on the surface of the earth ? Take radius of earth as `6.410^(6)` m, g on the surface of the earth as `9.8 m//s^(2)`.

Explanation

To find the altitude at which the acceleration due to gravity (g') is half of its value on the surface of the Earth (g), we can follow these steps:

### Step 1: Understand the relationship between g and g'
The acceleration due to gravity at a height \( h \) above the Earth's surface is given by the formula:
\[ g' = \frac{g \cdot R^2}{(R + h)^2} \]
where:
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