Question

At what height above the earth?s surface, the value of $g$ is half of its value on earth?s surface? Given its radius is 6400 km.

• A. 649.6 km
• B. 946.4 km
• C. 2649.6 km
• D. 624.6 km

Answer 1

Answer: (C)

2649.6 km

Answer 2

Here g = g/2
But g $=g\left(\frac{R}{R+h}\right)^{^2}$
$\therefore\quad \frac{g}{2}=g\left(\frac{R}{R+h}\right)^{^2}$ or $\left(\frac{R}{R+h}\right)^{^2}=\frac{1}{2}$
or $\quad \frac{R+h}{R}=\sqrt{2}$
or $h=\left(\sqrt{2}-1\right)R = 0.414 R = 0.414 ? 6400$
$= 2649.6$ km.