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%
From NCERT
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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%
From NCERT
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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 |
84%
From NCERT
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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 |
63%
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 $9.4×{10}^{3}$ km. The mass of mars is:
1.
2.
3.
4.

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%
From NCERT
Hints

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