Question

At what height from the surface of earth will the value of 'g' reduced to 64% from the value at the surface? Radius of earth = 6400 Km​

Answer 1

Answer: 1600 km from the surface

Explanation:

$E = \frac{GM}{R^{2} }\\g1 = \frac{GM}{R1^{2} } \\R1 = 6400 km\\g2 = 0.64g1\\\frac{g1}{g2} = \frac{\frac{GM}{R1^{2} } }{\frac{GM}{R2^{2} } } \\\frac{g1}{0.64g1} = \frac{R2^{2}}{R1^{2} }\\\frac{1}{0.64} = \frac{R2^{2}}{6400^{2} }\\\\\frac{1}{0.8} = \frac{R2}{6400}\\\\R2 = \frac{6400}{0.8}\\R2 = 8000 km$

Therefore, 8000 km - 6400 km = 1600 km from the surface