Q. At what height above the earth’s surface does the force of gravity decrease by 10%? The radius of the earth is 6400 km?
A) 345.60 km
B) 687.20 km
C) 1031.8 km
D) 12836.80 km
Explanation
(a) $g^{'} = g - \frac{10g}{100} - \frac{90}{100}g$
$g^{'} = g\frac{R^{2}}{(R + h)^{2}}\ or\ \ \ \frac{9}{10} = \frac{R^{2}}{(R + h)^{2}}$
or $\frac{3}{\sqrt{10}} = \frac{R}{R + h}$
or $h = \left( \sqrt{10} - 3 \right)R/3$
$\frac{(\sqrt{10} - 3) \times 6400}{3} = 345.60\ km$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.