Question

A man weighs $60kg$ at earth surface. At what height above the earths surface weight becomes $30kg$? (Given, radius of earth is $6400km$.)

• A. 2624 km
• B. 3000 km
• C. 2020 km
• D. none of these

Answer 1

Answer: (A)

From Newtons law of gravitation
$F=\frac{G{M}_{e}m}{R_e^2}$ ...(i)
where $G$ is gravitational constant,
$M_e$ the mass of earth,
$R_e$ the radius and
$m$ the mass of man.
Also, $F=mg$ = weight ...(ii)
From Eqs. (i) and (ii), we get
$W=\frac{G{M}_{e}m}{R_e^2}$
$\therefore \frac{W_1}{W_2}=\frac{R_2^2}{R_1^2}$
$=\frac{{\left(R_e+h\right)}^2}{R_e^2}$
Given, $W_1=60kg,W_2=30kg$
$\therefore \frac{60}{30}={\left(\frac{R_e+h}{R_e}\right)}^2$
Taking square root $\sqrt{2}=\frac{R_e+h}{R_e}$
$\Rightarrow \sqrt{2}{R}_e=R_e+h$
$\Rightarrow h=\sqrt{2}{R}_e-R_{e}h=1.41R_e-R_{e}h=0.41R_e$
Given, $R_e=6400km$
$\therefore h=0.41\times 6400=2624km$