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Q. No.Kepler's second law is based on:
| 1. | Newton's first law |
| 2. | Newton's second law |
| 3. | Special theory of relativity |
| 4. | Conservation of angular momentum |
Subtopic: Kepler's Laws |
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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: Kepler's Laws |
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Level 2: 60%+
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If Kepler's law of time periods were to be stated in terms of the average angular speed \(\omega\) of a planet in orbit and its orbital radius \(r,\) then:
1. \(\omega^2\propto r^3\)
2. \(\omega^2\propto {\dfrac{1}{r^3}}\)
3. \(\omega^2\propto r\)
4. \(\omega^2\propto {\dfrac{1}{r}}\)
1. \(\omega^2\propto r^3\)
2. \(\omega^2\propto {\dfrac{1}{r^3}}\)
3. \(\omega^2\propto r\)
4. \(\omega^2\propto {\dfrac{1}{r}}\)
Subtopic: Kepler's Laws |
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A geostationary satellite is taken to another orbit, radius of which is twice that of it earlier orbit. Its new time period would be:
1. \(48\sqrt{2}\text{ hours}\)
2. \(48\text{ hours}\)
3. \(\dfrac{48}{\sqrt{2}}\text{ hours}\)
4. \(24\text{ hours}\)
1. \(48\sqrt{2}\text{ hours}\)
2. \(48\text{ hours}\)
3. \(\dfrac{48}{\sqrt{2}}\text{ hours}\)
4. \(24\text{ hours}\)
Subtopic: Kepler's Laws |
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Level 2: 60%+
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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: Kepler's Laws |
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Level 2: 60%+
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A comet is orbiting the sun in a highly elliptical orbit. Which of the following quantities remains constant during its revolution?
1. Linear speed
2. Angular momentum
3. Angular speed
4. Kinetic energy
1. Linear speed
2. Angular momentum
3. Angular speed
4. Kinetic energy
Subtopic: 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: Kepler's Laws |
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Level 2: 60%+
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Two satellites \(A\) and \(B\) of masses \(200\) kg and \(400\) kg are revolving around the Earth at heights of \(600\) km and \(1600\) km respectively. If \(T_A\) and \(T_B\) are the time periods of \(A\) and \(B\) respectively, then the ratio \(\dfrac{T_A}{T_B}\) is:
(Given: radius of Earth = \(6400\) km, mass of Earth \(=6\times 10^{24}\) kg)
1. \(\left ( \dfrac{7}{8} \right )^{3} \)
2. \(\left ( \dfrac{7}{8} \right )^{3/2} \)
3. \(\left ( \dfrac{7}{8} \right )^{2/3} \)
4. \(\left ( \dfrac{7}{8} \right )^{1/3} \)
Subtopic: Kepler's Laws |
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If \(R\) is the radius of the orbit of a planet and \(T\) is the time period of the planet, then which of the following graphs correctly shows the motion of a planet revolving around the sun?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: 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: Kepler's Laws |
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