Question

A rocket is fired from the earth to the moon. The distance between the earth and the moon is $r$ and the mass of the earth is $81$ times the mass of the moon. The gravitational force on the rocket will be zero, when its distance from the moon is then

• A. $\frac{r}{20}$
• B. $\frac{r}{15}$
• C. $\frac{r}{10}$
• D. $\frac{r}{5}$

Answer 1

The correct option is C $\frac{r}{10}$

Net force on the rocket is zero. i.e. force due to the earth and force due to moon is same but in opposite direction.
$Fe=Fm$
$\frac{GMeMr}{r{e}^2}=\frac{GMmMr}{r{m}^2}$
$r$ is the total distance
$r=re+rm$
$Me=81Mm$
$\frac{a81MmMr}{r{e}^2}=\frac{GMmMr}{r{m}^2}$
$r_m=\frac{r_e}{g}$
$grm+rm=r\Rightarrow 10r_m=r$
$\Rightarrow r_m=\frac{r}{10}$