At what altitude in metre will acceleration due to gravity be 25% of that at earth's surface (Ra

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7.Gravitation

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At what altitude in metre will the acceleration due to gravity be $25\%$ of that at the earth's surface (Radius of earth $= R\, metre$)

A

$\frac{1}{4}R$

B

$R$

C

$\frac{3}{8}R$

D

$\frac{R}{2}$

Solution

(b) $g' = g{\left( {\frac{R}{{R + h}}} \right)^2}$ $⇒$$\frac{g}{4} = g{\left( {\frac{R}{{R + h}}} \right)^2}$ $⇒$ $\frac{1}{2} = \frac{R}{{R + h}}$

$⇒$ $R + h = 2R$

$h = R$

Standard 11

Physics

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