Question

An artificial satellite around a planet for which gravitational force $\left(F\right)$ varies with distance $r$ from its center as $F\propto r^2$ If $v_0$ its orbital speed. then

• A. $v_0\propto r^{-1/2}$
• B. $v_0\propto r^{3/2}$
• C. $v_0\propto r^{-3/2}$
• D. $v_0\propto r$

Answer 1

The correct option is B $v_0\propto r^{3/2}$

Here the gravitational force is directly proportional to the square law

so what do we get is....

$F=GMm.r^2$

so we get$:$

$m{v}^2/r=GMm.r^2$

Therefore$,$

$v^0=\sqrt{GM{r}^3}$

thus $v^0$ is directly proportional to $r^{3/2}$

Hence,

option $\left(B\right)$ is correct answer.