The orbital velocity of a body near the surfa | vedclass

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(B) The orbital velocity of a body near the surface of planet $A$ is given by $V_{A} = \sqrt{\frac{GM_{A}}{r_{A}}}$.The escape velocity of a body from

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$\frac{1}{2}$

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(B) The orbital velocity of a body near the surface of planet $A$ is given by $V_{A} = \sqrt{\frac{GM_{A}}{r_{A}}}$.The escape velocity of a body from the surface of planet $B$ is given by $V_{B} = \sqrt{\frac{2GM_{B}}{r_{B}}}$.According to the problem,$V_{A} = V_{B}$.Therefore,$\sqrt{\frac{GM_{A}}{r_{A}}} = \sqrt{\frac{2GM_{B}}{r_{B}}}$.Since the masses are equal $(M_{A} = M_{B} = M)$,we have $\sqrt{\frac{GM}{r_{A}}} = \sqrt{\frac{2GM}{r_{B}}}$.Squaring both sides,we get $\frac{GM}{r_{A}} = \frac{2GM}{r_{B}}$.This simplifies to $\frac{1}{r_{A}} = \frac{2}{r_{B}}$,which implies $\frac{r_{A}}{r_{B}} = \frac{1}{2}$.

The orbital velocity of a body near the surface of a planet $A$ is equal to the escape velocity of a body from the planet $B$. If the masses of planets $A$ and $B$ are the same,the ratio of their radii is

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