Q. No.\(T\) is the time period of revolution of a planet revolving around the sun in an orbit of mean radius \(R\). Identify the incorrect graph.
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2. |  |
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4. |  |
Subtopic: Â Kepler's Laws |
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A planet revolving in elliptical orbit has:
| (A) | a constant velocity of revolution. |
| (B) | the least velocity when it is nearest to the sun. |
| (C) | its areal velocity directly proportional to its velocity. |
| (D) | its areal velocity inversely proportional to its velocity. |
| (E) | to follow a trajectory such that the areal velocity is constant. |
Choose the correct answer from the options given below:
| 1. | (A) only | 2. | (D) only |
| 3. | (C) only | 4. | (E) only |
Subtopic: Â Kepler's Laws |
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The time period of a geostationary satellite is \(24~\text{hr}\) at a height \(6R_E\) \((R_E\) is the radius of the Earth) from the surface of the earth. The time period of another satellite whose height is \(2.5R_E\) from the surface will be:
| 1. | \(6\sqrt{2}~\text{hr}\) | 2. | \(12\sqrt{2}~\text{hr}\) |
| 3. | \(\frac{24}{2.5}~\text{hr}\) | 4. | \(\frac{12}{2.5}~\text{hr}\) |
Subtopic: Â Kepler's Laws |
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NEET - 2019
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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. \(T_{A}^2-{T}_{B}^2=\dfrac{\pi^2}{GM}\left({r}_{B}^3-4 {r}_{A}^3\right)\)
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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If the period of a satellite in a circular orbit of radius, \(R\) is \(T,\) then the period of another satellite in a circular orbit of radius, \(2R\) is:
1. \(2T\)
2. \(T/2\)
3. \(T/\sqrt8\)
4. \(\sqrt8T\)
1. \(2T\)
2. \(T/2\)
3. \(T/\sqrt8\)
4. \(\sqrt8T\)
Subtopic: Â Kepler's Laws |
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Two planets are in a circular orbit of radius \(R\) and \(4R\) about a star. At a specific time, the two planets and the star are in a straight line. If the period of the closest planet is \(T,\) then the star and planets will again be in a straight line after a minimum time:
2. \((4)^{\frac13}T\)
3. \(2T\)
4. \(8T\)
Subtopic: Â Kepler's Laws |
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NEET - 2022
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Given below are two statements:
| Assertion (A): | The time period of the revolution of a satellite around a planet is directly proportional to the radius of the orbit of the satellite. |
| Reason (R): | Artificial satellites do not follow Kepler's law of planetary motion. |
| 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. | Both (A) and (R) are False. |
Subtopic: Â Kepler's Laws |
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Assume that earth and mars move in circular orbits around the sun, with the martian orbit being \(1.52\) times the orbital radius of the earth. The length of the martian year in days is approximately:
(Take \((1.52)^{3/2}=1.87\))
| 1. | \(344\) days | 2. | \(684\) days |
| 3. | \(584\) days | 4. | \(484\) days |
Subtopic: Â Kepler's Laws |
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Given below are two statements:
| Statement I: | The kinetic energy of a planet is maximum when it is closest to the sun. |
| Statement II: | The time taken by a planet to move from the closest position (perihelion) to the farthest position (aphelion) is larger for a planet that is farther from the sun. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
Subtopic: Â Kepler's Laws |
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A planet moves around the sun in an elliptical orbit with the perihelion at \(P ,\) and aphelion at \(A\). Let the quantities be defined as follows: (for the planet)
The subscripts refer to the quantity measured at the perihelion \((P)\) or aphelion \((A)\): \(v_P\) is the speed at perihelion, \(K_A\) is the kinetic energy at aphelion, etc. Then,
1. \(K_A r^2_A = K_Pr^2_P\)
2. \(v_A r_A = v_P~r_P\)
3. \(U_Ar_A = U_P r_P\)
4. All the above are true
| \(r\) | distance from sun \(S\) |
| \(v\) | speed in orbit |
| \(K\) | kinetic energy |
| \(U\) | potential energy |
The subscripts refer to the quantity measured at the perihelion \((P)\) or aphelion \((A)\): \(v_P\) is the speed at perihelion, \(K_A\) is the kinetic energy at aphelion, etc. Then,
1. \(K_A r^2_A = K_Pr^2_P\)
2. \(v_A r_A = v_P~r_P\)
3. \(U_Ar_A = U_P r_P\)
4. All the above are true
Subtopic: Â Kepler's Laws |
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