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Byju's Answer

Standard XII

Physics

Kepler's Law

Two satellite...

Question

Two satellites of masses $m_{1}$ and $m_{2}$ ( $m_{1}$ > $m_{2}$ ) are revolving around earth in circular orbits of radii $r_{1}$ and $r_{2}$ ( $r_{1} = r_{2}$ ) respectively. Which of the following statements is true regarding their velocities $V_{1}$ and $V_{2}$ .

V_{1} = V_{2}

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V_{1} > V_{2}

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V_{1} < V_{2}

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\frac{V_{1}}{r_{1}} = \frac{V_{2}}{r_{2}}

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Solution

The correct options are
A $V_{1} = V_{2}$
D $\frac{V_{1}}{r_{1}} = \frac{V_{2}}{r_{2}}$
We know:

$V_{c} = \sqrt{\frac{G M}{r}}$
$V_{c} \propto \frac{1}{\sqrt{r}}$
Thus, critical velocity is independent of mass.
So, $V_{1} = V_{2}$
Also as $r_{1} = r_{2}$ , we see that option D is also correct.

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Two satellites of masses $m_{1}$ and $m_{2} (m_{1} > m_{2})$ are revolving round the earth in circular orbits of radius $r_{1}$ and $r_{2} (r_{1} > r_{2})$ respectively. Which of the following statements is true regarding their speeds $v_{1}$ and $v_{2}$ ?

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Two satellites of masses m1 and m2 (m1 > m2) are revolving around earth in circular orbits of radii r1 and r2 (r1=r2) respectively. Which of the following statements is true regarding their velocities V1 and V2.

The correct options are A V1=V2 D V1r1=V2r2We know: Vc=√GMrVc∝1√rThus, critical velocity is independent of mass.So, V1=V2Also as r1=r2, we see that option D is also correct.

Two satellites of masses $m_{1}$ and $m_{2}$ ( $m_{1}$ > $m_{2}$ ) are revolving around earth in circular orbits of radii $r_{1}$ and $r_{2}$ ( $r_{1} = r_{2}$ ) respectively. Which of the following statements is true regarding their velocities $V_{1}$ and $V_{2}$ .

The correct options are
A $V_{1} = V_{2}$
D $\frac{V_{1}}{r_{1}} = \frac{V_{2}}{r_{2}}$
We know:

$V_{c} = \sqrt{\frac{G M}{r}}$
$V_{c} \propto \frac{1}{\sqrt{r}}$
Thus, critical velocity is independent of mass.
So, $V_{1} = V_{2}$
Also as $r_{1} = r_{2}$ , we see that option D is also correct.