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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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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 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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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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The figure shows two concentric shells of masses \(m,~\) and \(m.~\) At which point a particle of mass \(m\) shall experience zero gravitational force because of them?
1. \(A\)
2. \(C\)
3. \(D\)
4. \(B\)
Subtopic: Newton's Law of Gravitation |
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Two objects of equal masses placed at certain distance from each other attracts each other with a force of \(F\). If one-third mass of one object is transferred to the other object, then the new force will be:
| 1. | \( \dfrac{2}{9}{F} \) | 2. | \(\dfrac{16}{9} F\) |
| 3. | \(\dfrac{8}{9} F\) | 4. | \(F\) |
Subtopic: Newton's Law of Gravitation |
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The gravitational force between two objects:
| 1. | occurs only when the objects have very different masses |
| 2. | is greater on the more massive of the two objects |
| 3. | is not an attractive force |
| 4. | increases in magnitude as the two objects approach each other |
Subtopic: Newton's Law of Gravitation |
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