Question

The altitude at which the weight of a body is only $64\%$ of its weight on the surface of the earth is (Radius of the earth $6,400km$)

• A. $1600M$
• B. $2Km$
• C. $160Km$
• D. $1600Km$

Answer 1

The correct option is B $2Km$

Given,

$R=6400km$

So, $g^{\prime }=g(1-\frac{2h}{R})=g-\frac{2gh}{R}\Rightarrow g-g^{\prime }=\frac{2gh}{R}$

Percentage decreases in weight,

$=\frac{mg-m{g}^{\prime }}{mg}\times 100=\frac{g-g}{g}\times 100=\frac{2gh}{gR}\times 100=\frac{2h}{R}\times 100\Rightarrow 64=\frac{2\times h}{6400}\times 100\Rightarrow h=2.048km$