Question

Two satellites $A$ and $B$ of the same mass are revolving around the earth in the concentric circular orbits such that the distance of satellite $B$ from the centre of the earth is thrice as compared to the distance of the satellite $A$ from the centre of the earth. The ratio of the centripetal force acting on $B$ as compared to that on $A$ is

• A. $\frac{1}{3}$
• B. $3$
• C. $\frac{1}{9}$
• D. $\frac{1}{\sqrt{3}}$

Answer 1

Answer: (C)

$\frac{1}{9}$

since centripetal force ($\frac{m{v}^2}{r}$) is obtained from gravitational force $F=\frac{GMm}{r^2}$
Since masses of satellites are same.hence,
$F\propto \frac{1}{r^2}$
$\frac{F_A}{F_B}={\left(\frac{r_B}{r_A}\right)}^2=3^2$
$\therefore F_B=\frac{1}{9}{F}_A$