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Q. No.If the angular momentum of a planet of mass \({m},\) moving around the sun in a circular orbit is \(L\) about the center of the sun, its areal velocity is:
1. \({ \dfrac L m}\)
2. \( \dfrac {4L} {m}\)
3. \(\dfrac L {2m}\)
4. \({ \dfrac {2L} m}\)
1. \({ \dfrac L m}\)
2. \( \dfrac {4L} {m}\)
3. \(\dfrac L {2m}\)
4. \({ \dfrac {2L} m}\)
Subtopic: Â Kepler's Laws |
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A planet revolving in an elliptical orbit has:
| (A) | A constant velocity of revolution. |
| (B) | Has the least velocity when it is nearest to the Sun. |
| (C) | Its areal velocity is directly proportional to its velocity. |
| (D) | Areal velocity is inversely proportional to its velocity. |
| (E) | To follow a trajectory such that the areal velocity is constant. |
Choose the correct option from the given ones:
| 1. | (A) only |
| 2. | (D) only |
| 3. | (C) only |
| 4. | (E) only |
Subtopic: Â Kepler's Laws |
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The distance between Sun and Earth is \(R\). The duration of the year if the distance between Sun and Earth becomes \(3R\) will be:
1. \(\sqrt {3}\) years
2. \(3\) years
3. \(9\) years
4. \(3\sqrt{3}\) years
1. \(\sqrt {3}\) years
2. \(3\) years
3. \(9\) years
4. \(3\sqrt{3}\) years
Subtopic: Â Kepler's Laws |
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Two satellites \(S_{1}\) and \(S_{2}\) are revolving in circular orbits around a planet with radius \(R_1=3200~\text{km}\) and \(R_2=800~\text{km}\) respectively. The ratio of the speed of the satellite \(S_{1}\) to the speed of the satellite \(S_{2}\) in their respective orbits would be:
1. \(\dfrac{1}{2}\)
2. \(\dfrac{1}{3}\)
3. \(\dfrac{1}{4}\)
4. \(\dfrac{2}{3}\)
1. \(\dfrac{1}{2}\)
2. \(\dfrac{1}{3}\)
3. \(\dfrac{1}{4}\)
4. \(\dfrac{2}{3}\)
Subtopic: Â Kepler's Laws |
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Level 3: 35%-60%
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Two planets \(A\) and \(B\) of equal masses are having their periods of revolution \(T_{A}\) and \(T_{B}\) such that \(T_{A}=2 {T}_{B} \). These planets are revolving in the circular orbits of radii \({r}_{A} \) and \(r_{B} \) respectively. Which of the following would be the correct relationship of their orbits?
| 1. | \(2 r_{A}^2=r_{B}^2 \) |
| 2. | \(r_{A}^3=2 r_{B}^3 \) |
| 3. | \(r_{A}^3=4{r}_{B}^3 \) |
| 4. | \(T_{A}^2-{T}_{B}^2=\dfrac{\pi^2}{GM}\left({r}_{B}^3-4 {r}_{A}^3\right) \) |
Subtopic: Â Kepler's Laws |
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The time period of a satellite revolving around the Earth in a given orbit is \(7\) hours. If the radius of the orbit is increased to three times its previous value, then the approximate new time period of the satellite will be:
1. \(40\) hours
2. \(36\) hours
3. \(30\) hours
4. \(25\) hours
1. \(40\) hours
2. \(36\) hours
3. \(30\) hours
4. \(25\) hours
Subtopic: Â Kepler's Laws |
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Consider the following statements:
Choose the incorrect statement from the given ones:
1. (A) only
2. (B) only
3. (C) only
4. (D) only
| (A) | Planets revolve around the Sun with constant linear speed. |
| (B) | The energy of a planet in an elliptical orbit is constant. |
| (C) | A satellite in circular motion has constant energy. |
| (D) | A body falling towards the Earth results in negligible displacement of the Earth. |
1. (A) only
2. (B) only
3. (C) only
4. (D) only
Subtopic: Â Kepler's Laws |
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If a planet at distance \(r\) from the sun takes \(200\) days to complete one revolution, what will be the orbital period of a planet at distance \( \dfrac{r}{4}\) from the sun?
1. \(50\) days
2. \(25\) days
3. \(100\) days
4. \(12.5\) days
1. \(50\) days
2. \(25\) days
3. \(100\) days
4. \(12.5\) days
Subtopic: Â Kepler's Laws |
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Level 1: 80%+
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Two planets \({A}\) and \({B}\) having masses \({m_1}\) and \({m_2}\) move around the sun in circular orbits of \({r_1}\) and \({r_2}\) radii respectively. If angular momentum of \({A}\) is \({L}\) and that of \({B}\) is \({3L},\) the ratio of time period \({(T_A/T_B)}\) is:
1. \({\frac{1}{27}\left(\frac{m_2}{m_1}\right)^3}\)
2. \({\left(\frac{r_1}{r_2}\right)^3}\)
3. \({\left(\frac{r_1}{r_2}\right)^{3\over 2}}\)
4. \({27\left(\frac{m_1}{m_2}\right)^3}\)
1. \({\frac{1}{27}\left(\frac{m_2}{m_1}\right)^3}\)
2. \({\left(\frac{r_1}{r_2}\right)^3}\)
3. \({\left(\frac{r_1}{r_2}\right)^{3\over 2}}\)
4. \({27\left(\frac{m_1}{m_2}\right)^3}\)
Subtopic: Â Kepler's Laws |
Level 3: 35%-60%
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