Question

Find the height above the surface of the earth where weight of a body becomes half.

• A. $(\sqrt{2}-1)R$
• B. $\frac{R}{2}$
• C. $\frac{R}{(\sqrt{2}+1)}$
• D. $\frac{R}{\sqrt{2}}$

Answer 1

Answer: (A), (C)

Given, weight of the body becomes half.

Let that height be $h$.

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

And, $g=\frac{GM}{{\left(R\right)}^2}\Rightarrow \frac{1}{2}=\frac{1}{{(1+\frac{h}{R})}^2}$

Hence, $h=(\sqrt{2}-1)R$

Multiplying numerator and denominator by $\sqrt{2}+1$

$h=\frac{R}{\sqrt{2}+1}$