Question

The masses of sun and earth are $M_s$ and $M_e$, respectively and the distance between them is $R_{es}$ then, the distance of a body of mass m, from the earth along the line towards the sun, where the sun's gravitational pull balances that of the earth is

• A. $\frac{R_{es}}{\sqrt{M_s/M_e}+1}$
• B. $\frac{R_{es}}{\sqrt{M_e/M_s}+1}$
• C. $\frac{R_{es}}{\sqrt{M_s/M_e}-1}$
• D. $\frac{R_{es}}{1-\sqrt{M_e/M_s}}$

Answer 1

The correct option is A $\frac{R_{es}}{\sqrt{M_s/M_e}+1}$

The net gravitational pull is zero i.e. $F_s=F_e....................\left(1\right)$
Let, the distance from earth is $x$. So, the distance from sun is $R_{es}-x$
Now,$F_s=\frac{G{M}_{s}m}{(R_{es}-x{)}^2}$ and
$F_e=\frac{G{M}_{e}m}{x^2}$.
Substituting in $\left(1\right)$ we get,
$\frac{G{M}_{s}m}{(R_{es}-x{)}^2}=F_e=\frac{G{M}_{e}Mm}{x^2}$
$\frac{M_{s}m}{(R_{es}-x{)}^2}=\frac{M_{e}m}{x^2}$
On further simplication, $x=\frac{R_{es}}{\sqrt{\frac{M_s}{M_e}}+1}$