The height at which the weight of a body beco | vedclass

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(D) The weight of a body at height $h$ is given by $W' = mg'$,where $g'$ is the acceleration due to gravity at that height.The formula for acceleratio

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$h = 2R$

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(D) The weight of a body at height $h$ is given by $W' = mg'$,where $g'$ is the acceleration due to gravity at that height.The formula for acceleration due to gravity at height $h$ is $g' = g \left(1 + \frac{h}{R}\right)^{-2}$.Given that the weight becomes $\frac{1}{9}$ of its weight on the surface,we have $g' = \frac{g}{9}$.Equating the two expressions: $\frac{g}{9} = \frac{g}{(1 + \frac{h}{R})^2}$.Taking the square root on both sides: $\frac{1}{3} = \frac{1}{1 + \frac{h}{R}}$.This implies $1 + \frac{h}{R} = 3$.Therefore,$\frac{h}{R} = 2$,which gives $h = 2R$.

The height at which the weight of a body becomes $\frac{1}{9}^{th}$ of its weight on the surface of the Earth (radius of Earth $R$) is:

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