Answer:
h = R/4 = 1.5925 x 10⁶ m = 1592.5 km
Explanation:
The variation in the value of acceleration due to gravity value with respect to the altitude is given by the following general formula:
[tex]g' = g(1-2\frac{h}{R})[/tex]
where,
h = altitude from surface of earth = ?
g = acceleration due to gravity on surface of earth = 9.81 m/s²
R = Radius of Earth = 6.37 x 10⁶ m
g' = acceleration due to gravity at given altitude = g/2
Therefore,
[tex]\frac{g}{2} = g(1-2\frac{h}{R})\\\\2\frac{h}{R} = 1-\frac{1}{2}\\\\2\frac{h}{R} = \frac{1}{2}\\\\\frac{h}{R} = \frac{1}{4}\\\\[/tex]
h = R/4 = 1.5925 x 10⁶ m = 1592.5 km