Statement (A) Two artificial satellites revol | vedclass

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(B) The time period $T$ of a satellite revolving around a planet is given by $T = 2\pi \sqrt{\frac{r^3}{GM}}$. Since both satellites are in the same c

Vedclass · Accepted Answer

$A, B$ are true,$C$ is false

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(B) The time period $T$ of a satellite revolving around a planet is given by $T = 2\pi \sqrt{\frac{r^3}{GM}}$. Since both satellites are in the same circular orbit,their orbital radius $r$ is the same,meaning their time periods are identical. Thus,Statement $(A)$ is true.The orbital velocity $v$ of a satellite is given by $v = \sqrt{\frac{GM}{r}}$. This shows that $v \propto \frac{1}{\sqrt{r}}$,meaning the orbital velocity is inversely proportional to the square root of the radius of the orbit. Thus,Statement $(B)$ is true.The escape velocity $v_e$ from a point at distance $r$ from the center of a planet is given by $v_e = \sqrt{\frac{2GM}{r}}$. Since $r = R + h$ (where $R$ is the radius of the planet and $h$ is the altitude),the escape velocity depends on the altitude $h$. Thus,Statement $(C)$ is false.

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