Q. No.A planet \((P_1)\) is having around the star of mass \(2M\) in the orbit of radius \(R\). Another planet \((P_2)\) is moving around another star of mass \(4M\) in a orbit of radius \(2R\). Ratio of the time periods of revolution of \(P_1\) and \(P_2\) is:
1. \(\dfrac{1}{2}\)
2. \(2\)
3. \(4\)
4. \(\dfrac{1}{4}\)
1. \(\dfrac{1}{2}\)
2. \(2\)
3. \(4\)
4. \(\dfrac{1}{4}\)
Subtopic: Kepler's Laws |
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Given below are two statements:
In the light of the above statements, choose the most appropriate answer from the options given below:
| Assertion (A): | The radius vector from the sun to a planet sweeps out equal areas in equal intervals of time and thus area velocity of planet is a constant. |
| Reason (R): | For a central force field the angular momentum is a constant. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Kepler's Laws |
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If a satellite orbiting the Earth is \(9\) times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon = \(27~\text{days}\) and gravitational attraction between the satellite and the moon is neglected.
1. \(27~\text{days}\)
2. \(3~\text{days}\)
3. \(81~\text{days}\)
4. \(1~\text{days}\)
1. \(27~\text{days}\)
2. \(3~\text{days}\)
3. \(81~\text{days}\)
4. \(1~\text{days}\)
Subtopic: Kepler's Laws |
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A satellite is launched into a circular orbit of radius \(R\) around the earth. A second satellite is launched into an orbit of radius \(1.03~R.\) the time period of revolutions of the second satellite is larger than the first one approximately by:
1. \(2.5\%\)
2. \(9\%\)
3. \(4.5\%\)
4. \(3\%\)
1. \(2.5\%\)
2. \(9\%\)
3. \(4.5\%\)
4. \(3\%\)
Subtopic: Kepler's Laws |
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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: Kepler's Laws |
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If the force acting on a planet is proportional to the \({r^{-2/7}},\) where \({r}\) is distance of the planet from the sun if time period is proportional to \({r^{x}},\) then the value of \(x\) is:
1. \(\dfrac{4}{7}\)
2. \(\dfrac{9}{14}\)
3. \(\dfrac{7}{9}\)
4. \(\dfrac{1}{9}\)
1. \(\dfrac{4}{7}\)
2. \(\dfrac{9}{14}\)
3. \(\dfrac{7}{9}\)
4. \(\dfrac{1}{9}\)
Subtopic: Kepler's Laws |
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If a planet at a distance \(r\) from the sun takes \(200\) days to complete one revolution, what will be the orbital period of a planet at a distance \( \dfrac{r}{4}\) from the sun?
1. \(50\text{ days}\)
2. \(25\text{ days}\)
3. \(100\text{ days}\)
4. \(12.5\text{ days}\)
1. \(50\text{ days}\)
2. \(25\text{ days}\)
3. \(100\text{ days}\)
4. \(12.5\text{ days}\)
Subtopic: 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: Kepler's Laws |
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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: 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: Kepler's Laws |
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