Question

At what height over the earth's pole does the freefall acceleration decreases by 1% ?

• A. $64km$
• B. $16km$
• C. $8km$
• D. $32km$

Answer 1

Answer: (D)

$32km$

$m{g}^{\prime }=\frac{GMm}{R^2+h^2}$

$mg=\frac{GMm}{R^2}$

$\frac{g^{\prime }}{g}=\frac{R^2}{R^2+h^2}$

$\frac{g^{\prime }}{g}=\left(R^2\right)(R^2+h^2{)}^{-2}$

$\frac{g^{\prime }}{g}=(1+\frac{h^2}{r^2}{)}^{-2}$

Expanding using binomial expansion and neglecting higher terms,

$\frac{g^{\prime }}{g}=(1-\frac{2h}{R})=\frac{99}{100}orh=32km$