# 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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The radii of circular orbits of two satellites A and B of the earth are $$4R$$ and $$R$$ respectively. If the speed of satellite A is $$3v,$$ then the speed of satellite B will be:
1. $$3v/4$$
2. $$6v$$
3. $$12v$$
4. $$3v/2$$

Subtopic:  Satellite |
58%
From NCERT
AIPMT - 2010
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An infinite number of bodies, each of mass $$2$$ kg are situated on the $$x\text-$$axis at distances $$1 m, ~2m, ~4m, ~8m, \ldots \ldots .$$respectively, from the origin. The resulting gravitational potential due to this system at the origin will be:
 1 $$-\frac{8}{3}{G}$$ 2 $$-\frac{4}{3} {G}$$ 3 $$-4 {G}$$ 4 $$-{G}$$
Subtopic:  Gravitational Potential |
69%
From NCERT
AIPMT - 2013
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A body of mass $$m$$ is taken from the Earth’s surface to the height equal to twice the radius $$(R)$$ of the Earth. The change in potential energy of the body will be:

 1 $$\frac{2}{3}mgR$$ 2 $$3mgR$$ 3 $$\frac{1}{3}mgR$$ 4 $$2mgR$$
Subtopic:  Gravitational Potential Energy |
76%
From NCERT
AIPMT - 2013
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A remote sensing satellite of earth revolves in a circular orbit at a height of $$0.25 \times10^6~\text{m}$$ above the surface of the earth. If Earth’s radius is $$6.38\times10^6~\text{m}$$ and $$g=9.8~\text{ms}^{-2}$$, then the orbital speed of the satellite is:
1. $$7.76~\text{kms}^{-1}$$
2. $$8.56~\text{kms}^{-1}$$
3. $$9.13~\text{kms}^{-1}$$
4. $$6.67~\text{kms}^{-1}$$

Subtopic:  Orbital velocity |
51%
From NCERT
NEET - 2015
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A satellite of mass $$m$$ is orbiting the earth (of radius $$R$$) at a height $$h$$ from its surface. What is the total energy of the satellite in terms of $$g_0?$$
($$g_0$$ is the value of acceleration due to gravity at the earth's surface)

 1 $$\frac{mg_0R^2}{2(R+h)}$$ 2 $$-\frac{mg_0R^2}{2(R+h)}$$ 3 $$\frac{2mg_0R^2}{(R+h)}$$ 4 $$-\frac{2mg_0R^2}{(R+h)}$$
Subtopic:  Gravitational Potential Energy |
77%
From NCERT
NEET - 2016
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Starting from the centre of the earth, having radius $$R,$$ the variation of $$g$$ (acceleration due to gravity) is shown by:

 1 2 3 4

Subtopic:  Acceleration due to Gravity |
85%
From NCERT
NEET - 2016
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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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A body weighs $$63$$ N on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth?
1. $$98$$ N
2. $$35$$ N
3. $$63$$ N
4. $$28$$ N

Subtopic:  Acceleration due to Gravity |
73%
From NCERT
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Assuming the earth to be a sphere of uniform mass density, how much would a body weigh halfway down to the centre of the earth if it weighed $$250$$ N on the surface?
1. $$250$$ N
2. $$125$$ N
3. $$175$$ N
4. $$145$$ N

Subtopic:  Acceleration due to Gravity |
83%
From NCERT
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