(A) The acceleration due to gravity at a height $h$ above the surface of the earth is given by the formula: $g' = g \left( \frac{R}{R+h} \right)^2$.Gi

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(A) The acceleration due to gravity at a height $h$ above the surface of the earth is given by the formula: $g' = g \left( \frac{R}{R+h} \right)^2$.Given that $g' = \frac{g}{9}$,we substitute this into the equation:$\frac{g}{9} = g \left( \frac{R}{R+h} \right)^2$.Dividing both sides by $g$,we get: $\frac{1}{9} = \left( \frac{R}{R+h} \right)^2$.Taking the square root of both sides: $\frac{1}{3} = \frac{R}{R+h}$.Cross-multiplying gives: $R + h = 3R$.Therefore,$h = 3R - R = 2R$.

Class 11 Physics Gravitation Acceleration Due to Gravity and its Variation

Medium

The height at which the acceleration due to gravity becomes $\frac{g}{9}$ (where $g$ = the acceleration due to gravity on the surface of the earth) in terms of $R$,the radius of the earth,is

AIEEE 2009 All AIEEE

A
$2R$
B
$\frac{R}{\sqrt{2}}$
C
$\frac{R}{2}$
D
$\sqrt{2}R$

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Acceleration Due to Gravity and its Variation

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The height at which the acceleration due to gravity becomes $\frac{g}{9}$ (where $g$ = the acceleration due to gravity on the surface of the earth) in terms of $R$,the radius of the earth,is

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