Q. At what distance from the centre of the earth, the value of acceleration due to gravity $g$ will be half that on the surface ($R$ = radius of earth)
A) $2\ R$
B) $R$
C) $1.414\ R$
D) $0.414\ R$
Explanation
(c) $g^{'} = g\left( \frac{R}{R + h} \right)^{2} \Rightarrow \frac{1}{\sqrt{2}} = \frac{R}{R + h}$
$\Rightarrow R + h = \sqrt{2}R \Rightarrow h = \left( \sqrt{2} - 1 \right)R = 0.414R$
Hence, distance from centre $= R + 0.414\ R = 1.414\ R$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.