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 $6400km$.

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

Answer 1

Answer: (C)

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