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

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$5$

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(C) The acceleration due to gravity $g'$ at a height $h$ from the surface of the earth is given by the formula: $g' = g \left( \frac{R}{R+h} ight)^2$,where $g$ is the acceleration due to gravity on the surface of the earth and $R$ is the radius of the earth.Given: $h = (\sqrt{2}-1)R$ and $g = 10 \ m \ s^{-2}$.Substituting the value of $h$ in the formula:$g' = g \left( \frac{R}{R + (\sqrt{2}-1)R} ight)^2$$g' = g \left( \frac{R}{R + \sqrt{2}R - R} ight)^2$$g' = g \left( \frac{R}{\sqrt{2}R} ight)^2$$g' = g \left( \frac{1}{\sqrt{2}} ight)^2$$g' = g 	imes \frac{1}{2}$$g' = \frac{10}{2} = 5 \ m \ s^{-2}$.

The acceleration due to gravity at a height of $(\sqrt{2}-1) R$ from the surface of the earth is (Acceleration due to gravity on the surface of the earth $= 10 \ m \ s^{-2}$ and $R$ is radius of the earth). (in $m \ s^{-2}$)

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