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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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Kepler's third law states that square of the period of revolution \((T)\) of a planet around the sun, is proportional to the third power of average distance \(r\) between the sun and planet i.e. \(T^2=Kr^3,\) here \(K\) is constant. If the masses of the sun and planet are \(M\) and \(m\) respectively, then as per Newton's law of gravitation, the force of attraction between them is \(F=\dfrac{GMm}{r^2}, \) here \(G\) is gravitational constant. The relation between \(G\) and \(K\) is described as:
1. \(GK=4\pi^2\)
2. \(GMK=4\pi^2\)
3. \(K=G\)
4. \(K=\dfrac{1}{G}\)
1. \(GK=4\pi^2\)
2. \(GMK=4\pi^2\)
3. \(K=G\)
4. \(K=\dfrac{1}{G}\)
Subtopic: Kepler's Laws |
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The time period of a geostationary satellite is \(24\text{ h}\) 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. \(6\sqrt2\text{ h}\)
2. \(12\sqrt2\text{ h}\)
3. \(\dfrac{24}{2.5}\text{ h}\)
4. \(\dfrac{12}{2.5}\text{ h}\)
Subtopic: Kepler's Laws |
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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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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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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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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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