What will be the acceleration due to gravity at height h if h >> R. Where R is radius of earth ….

Q: What will be the acceleration due to gravity at height h if h >> R. Where R is radius of earth and g is acceleration due to gravity on the surface of earth

(a) $\frac{g}{(1+\frac{h}{R})^2}$

(b) $g(1-\frac{2h}{R})$

(c) $\frac{g}{(1-\frac{h}{R})^2}$

(d) $g(1-\frac{h}{R})$

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Ans: (a)

Sol: Acceleration due to gravity near the surface of earth ,

$\displaystyle g = \frac{G M}{R^2} $

Acceleration due to gravity at the height h above the surface of earth ,

$\displaystyle g’ = \frac{G M}{(R+h)^2} $

On dividing ,

$\displaystyle \frac{g’}{g} = \frac{R^2}{(R+h)^2} $

$\displaystyle \frac{g’}{g} = \frac{R^2}{R^2(1+\frac{h}{R})^2} $

$\displaystyle \frac{g’}{g} = \frac{1}{(1+\frac{h}{R})^2} $

$\displaystyle g’ = \frac{g}{(1+\frac{h}{R})^2} $