Two planets A and B are orbiting around the s | vedclass

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(C) The orbital speed $v$ of a planet at a distance $r$ from the sun is given by the formula $v = \sqrt{\frac{GM}{r}}$, where $G$ is the gravitational

Vedclass · Accepted Answer

$V/15$

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(C) The orbital speed $v$ of a planet at a distance $r$ from the sun is given by the formula $v = \sqrt{\frac{GM}{r}}$, where $G$ is the gravitational constant and $M$ is the mass of the sun.From this formula, we can see that $v \propto \frac{1}{\sqrt{r}}$.Therefore, the ratio of the orbital speeds of planets $A$ and $B$ is given by $\frac{v_B}{v_A} = \sqrt{\frac{r_A}{r_B}}$.Given that $r_B = 225 r_A$, we substitute this into the ratio:$\frac{v_B}{v_A} = \sqrt{\frac{r_A}{225 r_A}} = \sqrt{\frac{1}{225}} = \frac{1}{15}$.Since the orbital speed of planet $A$ is $V$, we have $v_A = V$.Thus, $v_B = \frac{v_A}{15} = \frac{V}{15}$.

Two planets $A$ and $B$ are orbiting around the sun. The distances of the two planets $A$ and $B$ from the sun are $r_A$ and $r_B$ respectively. Also $r_B = 225 r_A$. If the orbital speed of the planet $A$ is $V$, then the orbital speed of planet $B$ will be

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