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 $=1.5\times 10^{11}m)$

• 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)

$r=1.5\times 10^{i1}m$
At neutral point, $\frac{G{M}_{E}m}{x^2}=\frac{G{M}_{S}m}{(r-x{)}^2}$
$6\times 10^{24}(r-x{)}^2=2\times 10^{30}\left(x^2\right)$
$\frac{r-x}{x}={\left(\frac{1}{3}\times 10^6\right)}^{\frac{1}{2}}\Rightarrow x=\frac{1.5\times 10^{11}\times \sqrt{3}}{10^3}$
$\therefore x=2.6\times 10^{8}m$