- 1(current)
Q. No.The angular momentum of a planet of mass \(m,\) moving around the sun (mass: \(M\gg m\)) in an orbit of radius \(r\) is proportional to:
| 1. | \(mr\) | 2. | \(\dfrac{m}{r}\) |
| 3. | \(m\sqrt r\) | 4. | \(\dfrac{m}{\sqrt r}\) |
Subtopic: Â Kepler's Laws |
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Given below are two statements:
| Assertion (A): | The ratio \(R^3/T^2,\) where \(R\) is the radius of the orbit and \(T\) is the time period in the orbit of a satellite of the earth, depends only on the mass of the earth, and not on that of the satellite. |
| Reason (R): | This can be easily concluded by the application of Newton's law of gravitation together with Newton's laws of motion to the motion of the satellite in orbit. |
| 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: Â Kepler's Laws |
 65%
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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 |
 67%
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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 |
 70%
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If the earth were to move around the sun in an orbit with twice its present radius, then its new time period of revolution will be:
1. \(1~\text{year}\)
2. \(\sqrt2~\text{year}\)
3. \(2~\text{year}\)
4. \(2\sqrt2~\text{year}\)
1. \(1~\text{year}\)
2. \(\sqrt2~\text{year}\)
3. \(2~\text{year}\)
4. \(2\sqrt2~\text{year}\)
Subtopic: Â Kepler's Laws |
 74%
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The path of a particle moving in the earth's gravitational field (in outer space) is:
(A) a straight line
(B) an ellipse
(C) a parabola
(D) a hyperbola
Choose the correct statements from the ones given above:
(A) a straight line
(B) an ellipse
(C) a parabola
(D) a hyperbola
Choose the correct statements from the ones given above:
| 1. | A or B |
| 2. | A or B or C |
| 3. | A or B or D |
| 4. | A or B or C or D |
Subtopic: Â Kepler's Laws |
 58%
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A small light asteroid moves along the path: \(y=\dfrac{x^2}{4}\)
under the gravitation of a small dense star, the areal-velocity of the asteroid with respect to the star is \(1\) unit.
The unit of length is \(1,\) that of mass is \(1\) and time is also \(1.\) The value of Newton's gravitational constant \(G\) is \(4\pi^2\) (in these units). All answers must be expressed in these units. The mass of the asteroid is \(m~(m\ll1).\) Assume that the first two laws of Kepler are valid for the parabolic orbits also.
The star is located at:
1. \((0,0)\)
2. \((0,1)\)
3. \((0,-1)\)
4. \((0,2)\)
under the gravitation of a small dense star, the areal-velocity of the asteroid with respect to the star is \(1\) unit.
The unit of length is \(1,\) that of mass is \(1\) and time is also \(1.\) The value of Newton's gravitational constant \(G\) is \(4\pi^2\) (in these units). All answers must be expressed in these units. The mass of the asteroid is \(m~(m\ll1).\) Assume that the first two laws of Kepler are valid for the parabolic orbits also.
The star is located at:
1. \((0,0)\)
2. \((0,1)\)
3. \((0,-1)\)
4. \((0,2)\)
Subtopic: Â Kepler's Laws |
 54%
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A small light asteroid moves along the path: \(y=\dfrac{x^2}{4}\)
under the gravitation of a small dense star, the areal-velocity of the asteroid with respect to the star is \(1\) unit.
The unit of length is \(1,\) that of mass is \(1\) and time is also \(1.\) The value of Newton's gravitational constant \(G\) is \(4\pi^2\) (in these units). All answers must be expressed in these units. The mass of the asteroid is \(m~(m\ll1).\) Assume that the first two laws of Kepler are valid for the parabolic orbits also.
The speed of the asteroid, when it is fastest, is:
1. \(1\)
2. \(\pi\)
3. \(2\)
4. \(2\pi\)
under the gravitation of a small dense star, the areal-velocity of the asteroid with respect to the star is \(1\) unit.
The unit of length is \(1,\) that of mass is \(1\) and time is also \(1.\) The value of Newton's gravitational constant \(G\) is \(4\pi^2\) (in these units). All answers must be expressed in these units. The mass of the asteroid is \(m~(m\ll1).\) Assume that the first two laws of Kepler are valid for the parabolic orbits also.
The speed of the asteroid, when it is fastest, is:
1. \(1\)
2. \(\pi\)
3. \(2\)
4. \(2\pi\)
Subtopic: Â Kepler's Laws |
 52%
From NCERT
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A small light asteroid moves along the path: \(y=\dfrac{x^2}{4}\)
under the gravitation of a small dense star, the areal-velocity of the asteroid with respect to the star is \(1\) unit.
The unit of length is \(1,\) that of mass is \(1\) and time is also \(1.\) The value of Newton's gravitational constant \(G\) is \(4\pi^2\) (in these units). All answers must be expressed in these units. The mass of the asteroid is \(m~(m\ll1).\) Assume that the first two laws of Kepler are valid for the parabolic orbits also.
The mass of the star is:
under the gravitation of a small dense star, the areal-velocity of the asteroid with respect to the star is \(1\) unit.
The unit of length is \(1,\) that of mass is \(1\) and time is also \(1.\) The value of Newton's gravitational constant \(G\) is \(4\pi^2\) (in these units). All answers must be expressed in these units. The mass of the asteroid is \(m~(m\ll1).\) Assume that the first two laws of Kepler are valid for the parabolic orbits also.
The mass of the star is:
| 1. | \(\dfrac{4}{\pi^2}\) | 2. | \(\dfrac{1}{4\pi^2}\) |
| 3. | \(\dfrac{2}{\pi^2}\) | 4. | \(\dfrac{1}{2\pi^2}\) |
Subtopic: Â Kepler's Laws |
 52%
From NCERT
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A small light asteroid moves along the path: \(y=\dfrac{x^2}{4}\)
under the gravitation of a small dense star, the areal-velocity of the asteroid with respect to the star is \(1\) unit.
The unit of length is \(1,\) that of mass is \(1\) and time is also \(1.\) The value of Newton's gravitational constant \(G\) is \(4\pi^2\) (in these units). All answers must be expressed in these units. The mass of the asteroid is \(m~(m\ll1).\) Assume that the first two laws of Kepler are valid for the parabolic orbits also.
If a small planet were to orbit the star in a circular orbit of radius \(1\) unit, its time period will be:
1. \(2\pi\)
2. \(\pi\)
3. \(\sqrt2\pi\)
4. \(\dfrac{\pi}{\sqrt2}\)
under the gravitation of a small dense star, the areal-velocity of the asteroid with respect to the star is \(1\) unit.
The unit of length is \(1,\) that of mass is \(1\) and time is also \(1.\) The value of Newton's gravitational constant \(G\) is \(4\pi^2\) (in these units). All answers must be expressed in these units. The mass of the asteroid is \(m~(m\ll1).\) Assume that the first two laws of Kepler are valid for the parabolic orbits also.
If a small planet were to orbit the star in a circular orbit of radius \(1\) unit, its time period will be:
1. \(2\pi\)
2. \(\pi\)
3. \(\sqrt2\pi\)
4. \(\dfrac{\pi}{\sqrt2}\)
Subtopic: Â Kepler's Laws |
 63%
From NCERT
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Q. No.
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