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 $$S$$ is moving in an elliptical orbit around the earth. If the mass of the satellite is very small as compared to the mass of the earth, then:

 1 The angular momentum of $$S$$ about the centre of the earth changes in direction, but its magnitude remains constant. 2 The total mechanical energy of $$S$$ varies periodically with time. 3 The linear momentum of $$S$$ remains constant in magnitude. 4 The acceleration of $$S$$ is always directed towards the centre of the earth.
Subtopic:  Orbital velocity |
57%
From NCERT
NEET - 2015
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Kepler's third law states that the square of the period of revolution ($$T$$) of a planet around the sun, is proportional to the third power of average distance $$r$$ between the sun and planet i.e. $$T^2 = Kr^3$$, here $$K$$ is constant. If the masses of the sun and planet are $$M$$ and $$m$$ respectively, then as per Newton's law of gravitation, the force of attraction between them is $$F = \frac{GMm}{r^2},$$ here $$G$$ is the gravitational constant. The relation between $$G$$ and $$K$$ is described as:
1. $$GK = 4\pi^2$$
2. $$GMK = 4\pi^2$$
3. $$K =G$$
4. $$K = \frac{1}{G}$$

Subtopic:  Kepler's Laws |
79%
From NCERT
NEET - 2015
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Two spherical bodies of masses $$M$$ and $$5M$$ and radii $$R$$ and $$2R$$ are released in free space with initial separation between their centres equal to $$12R.$$ If they attract each other due to gravitational force only, then the distance covered by the smaller body before the collision is:

 1 $$2.5R$$ 2 $$4.5R$$ 3 $$7.5R$$ 4 $$1.5R$$

Subtopic:  Newton's Law of Gravitation |
60%
From NCERT
NEET - 2015
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A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would Earth (mass $$= 5.98\times 10^{24}~\text{kg}$$) have to be compressed to be a black hole?
1. $$10^{-9}~\text{m}$$
2. $$10^{-6}~\text{m}$$
3. $$10^{-2}~\text{m}$$
4. $$100​~\text{m}$$

Subtopic:  Escape velocity |
61%
From NCERT
AIPMT - 2014
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Dependence of intensity of gravitational field $$(\mathrm{E})$$ of the earth with distance $$(\mathrm{r})$$ from the centre of the earth is correctly represented by: (where $$\mathrm{R}$$ is the radius of the earth)

 1 2 3 4
Subtopic:  Gravitational Field |
64%
From NCERT
AIPMT - 2014
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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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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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The radius of a planet is twice the radius of the earth. Both have almost equal average mass densities. If $$V_P$$ and $$V_E$$ are escape velocities of the planet and the earth, respectively, then:
1. $$V_P = 1.5 V_E$$
2. $$V_P = 2V_E$$
3. $$V_E = 3 V_P$$
4. $$V_E = 1.5 V_P$$
Subtopic:  Escape velocity |
80%
From NCERT
NEET - 2013
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A particle of mass $$m$$ is kept at rest at a height $$3R$$ from the surface of the earth, where $$R$$ is the radius of earth and $$M$$ is the mass of the earth. The minimum speed with which it should be projected, so that it does not return, is:
($$g$$ is the acceleration due to gravity on the surface of the earth)
 1 $$\left(\frac{{GM}}{2 {R}}\right)^{\frac{1}{2}}$$ 2 $$\left(\frac{{g} R}{4}\right)^{\frac{1}{2}}$$ 3 $$\left(\frac{2 g}{R}\right)^{\frac{1}{2}}$$ 4 $$\left(\frac{G M}{R}\right)^{\frac{1}{2}}$$