Question

At what distance above the surface of earth, the gravitational force will be reduced by $10\%$, if the radius of earth is $6370$ Km.

• A. $344Km$
• B. $450Km$
• C. $750Km$
• D. $650Km$

Answer 1

Answer: (A)

Gravitational force on the earth surface,

$F_{G_s}=\frac{GMm}{R^2}$

Gravitational force at a height 'h' above,

$F_{G_h}=\frac{GMm}{(R+h{)}^2}$

G.T. $F_{G_h}=\frac{90}{100}\left(F_{G_S}\right)$

$\Rightarrow \frac{GMm}{(R+h{)}^2}=\frac{9}{10}\left(\frac{GMm}{R^2}\right)$

$\Rightarrow R+h=\sqrt{\frac{10}{9}}\left(R\right)$

$\Rightarrow 6370+h=\frac{3.162}{3}\left(6370\right)$

$\Rightarrow h=\frac{0.162\times 6370}{3}=344$ km