If \(A\) is the areal velocity of a planet of mass \(M,\) then its angular momentum is:

1. \(\frac{M}{A}\) 2. \(2MA\)
3. \(A^2M\) 4. \(AM^2\)
Subtopic:  Kepler's Laws |
 74%
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The figure shows the elliptical orbit of a planet \(m\) about the sun \(\mathrm{S}.\) The shaded area \(\mathrm{SCD}\) is twice the shaded area \(\mathrm{SAB}.\) If \(t_1\) is the time for the planet to move from \(\mathrm{C}\) to \(\mathrm{D}\) and \(t_2\) is the time to move from \(\mathrm{A}\) to \(\mathrm{B},\) then:
           

1. \(t_1>t_2\) 2. \(t_1=4t_2\)
3. \(t_1=2t_2\) 4. \(t_1=t_2\)


Subtopic:  Kepler's Laws |
 71%
From NCERT
AIPMT - 2009
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Let the speed of the planet at the perihelion \(P\) in figure shown below be \(v_{_P}\) and the Sun-planet distance \(\mathrm{SP}\) be \(r_{_P}.\) Relation between \((r_{_P},~v_{_P})\) to the corresponding quantities at the aphelion \((r_{_A},~v_{_A})\) is:

              
1. \(v_{_P} r_{_P} =v_{_A} r_{_A}\)
2. \(v_{_A} r_{_P} =v_{_P} r_{_A}\)
3. \(v_{_A} v_{_P} = r_{_A}r_{_P}\)
4. none of these

Subtopic:  Kepler's Laws |
 78%
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Which of the following quantities remain constant in a planetary motion (consider elliptical orbits) as seen from the sun?
1. speed
2. angular speed
3. kinetic energy
4. angular momentum

Subtopic:  Kepler's Laws |
 85%
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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:
           

1. \((4)^2T\) 2. \((4)^{\frac13}T\)
3. \(2T\) 4. \(8T\)
Subtopic:  Kepler's Laws |
 62%
From NCERT
NEET - 2022
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The planet Mars has two moons, Phobos and Delmos. Phobos has a period of \(7\) hours, \(39\) minutes and an orbital radius of 9.4×103 km. The mass of mars is:
1. 6.48×1023 kg
2. 6.48×1025 kg
3. 6.48×1020 kg
4. 6.48×1021 kg

Subtopic:  Satellite |
From NCERT
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The force of gravitation between a particle \(A,\) and another particle \(B\) when separated by a distance \(r\) is \(F_{AB};\) while the force between a particle \(C\) and \(A\) separated by the same distance is \(4F_{AB}.\) The ratio of the masses of \(B\) and \(C\) is:
1. \(4\)
2. \(2\)
3. \(\frac12\)
4. \(\frac14\)
Subtopic:  Newton's Law of Gravitation |
 81%
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Three equal masses of \(m\) kg each are fixed at the vertices of an equilateral triangle \(ABC.\) What is the force acting on a mass \(2m\) placed at the centroid \(G\) of the triangle
(
Take \(AG=BG=CG=1\) m.)

       

1. \(Gm^2(\hat{i}+\hat{j})\)
2. \(Gm^2(\hat{i}-\hat{j})\)
3. zero
4. \(2Gm^2(\hat{i}+\hat{j})\)

Subtopic:  Newton's Law of Gravitation |
 82%
From NCERT
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Two spheres of masses \(m\) and \(M\) are situated in air and the gravitational force between them is \(F.\) If the space around the masses is filled with a liquid of specific density \(3,\) the gravitational force will become:
1. \(3F\)
2. \(F\)
3. \(F/3\)
4. \(F/9\)

Subtopic:  Newton's Law of Gravitation |
 82%
From NCERT
AIPMT - 2003
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If a particle is projected vertically upward with a speed \(u,\) and rises to a maximum altitude \(h\) above the earth's surface then (\(g=\) acceleration due to gravity at surface)

1. \(h>\frac{u^2}{2g}\)
2. \(h=\frac{u^2}{2g}\)
3. \(h<\frac{u^2}{2g}\)
4. Any of the above maybe true, depending on the earth's radius
Subtopic:  Acceleration due to Gravity |
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