Question

A rocket is fired from the earth towards the sun. At what distance from the earth's centre is the gravitational force on the rocket zero? (Mass of the Sun $=2 \times 10^{00} kg$, Mass of the earth $=6 \times 10^{24} kg ,$ orbital radius $\left.=1.5 \times 10^{11} m \right)$

• A. $2.6 \times 10^{6} m$
• B. $2.6 \times 10^{7} m$
• C. $2.6 \times 10^{8} m$
• D. $2.6 \times 10^{9} m$

Answer 1

Answer: (C)

$r=1.5 \times 10^{i 1} m$
At neutral point, $\frac{G M_{E} m}{x^{2}}=\frac{G M_{S} m}{(r-x)^{2}}$
$6 \times 10^{24}(r-x)^{2}=2 \times 10^{30}\left(x^{2}\right)$
$\frac{r-x}{x}=\left(\frac{1}{3} \times 10^{6}\right)^{\frac{1}{2}} \Rightarrow x=\frac{1.5 \times 10^{11} \times \sqrt{3}}{10^{3}}$
$\therefore x=2.6 \times 10^{8} m$