Q. A body is taken to a height of $nR$ from the surface of the earth. The ratio of the acceleration due to gravity on the surface to that at the altitude is
A) ${(n + 1)}^{2}$
B) $(n + 1)^{- 2}$
C) ${(n + 1)}^{- 1}$
D) $(n + 1)$
Explanation
(a) Acceleration due to gravity at a height above the earth surface
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$\ \ \ \ \ \ \ \ \ \ g^{''} = g\left( \frac{R}{R + h} \right)^{2}$
$\ \ \ \ \ \ \ \ \ \ \frac{g}{g^{''}} = \left( \frac{R + h}{R} \right)^{2}$
$\ \ \ \ \ \ \ \ \ \ \frac{g}{g^{''}} = \left( \frac{R + nR}{R} \right)^{2}$
$\ \ \ \ \ \ \ \ \ \frac{g}{g^{''}} = (1 + n)^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.