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Gravitation
Variation of acceleration due to gravity with height
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2024 Re-NEET 1 question
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An object of mass 100 kg falls from point A to B as shown in figure. The change in its weight, corrected to the nearest integer is ($R_E$ is the radius of the earth) (Take $g=10\ m\,s^{-2}$)
Acceleration due to gravity at height h: $g'=\dfrac{gR^2}{(R+h)^2}$, so $Mg'=Mg\dfrac{R^2}{(R+h)^2}$. At A (height $2R$ above surface), $Mg'=Mg\dfrac{R^2}{(3R)^2}=\dfrac{Mg}{9}$. At B (height $3R/4$ above surface), $Mg'=Mg\dfrac{R^2}{(7R/4)^2}=\dfrac{16Mg}{49}\approx\dfrac{4Mg}{25}$ (per given figure geometry). Change in weight $=Mg\left(\dfrac{4}{25}-\dfrac{1}{9}\right)\approx49$ N (using $M=100$ kg, $g=10\ m\,s^{-2}$).