# 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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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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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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Two satellites of Earth, $$S_1$$, and $$S_2$$, are moving in the same orbit. The mass of $$S_1$$ is four times the mass of $$S_2$$. Which one of the following statements is true?

 1 The time period of $$S_1$$ is four times that of $$S_2$$. 2 The potential energies of the earth and satellite in the two cases are equal. 3 $$S_1$$ and $$S_2$$ are moving at the same speed. 4 The kinetic energies of the two satellites are equal.

Subtopic:  Satellite |
67%
From NCERT
AIPMT - 2007
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A body weighs $$200$$ N on the surface of the earth. How much will it weigh halfway down the centre of the earth?

 1 $$100$$ N 2 $$150$$ N 3 $$200$$ N 4 $$250$$ N
Subtopic:  Acceleration due to Gravity |
80%
From NCERT
NEET - 2019
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If the mass of the sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following statements would not be correct?

 1 Raindrops would drop faster. 2 Walking on the ground would become more difficult. 3 Time period of a simple pendulum on the earth would decrease. 4 Acceleration due to gravity $$(g)$$  on earth would not change.
Subtopic:  Acceleration due to Gravity |
73%
From NCERT
NEET - 2018
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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 |
86%
From NCERT
NEET - 2016
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If the radius of a planet is $$R$$ and its density is $$\rho$$, the escape velocity from its surface will be:
1. $$v_e\propto \rho R$$
2. $$v_e\propto \sqrt{\rho} R$$
3. $$v_e\propto \frac{\sqrt{\rho}}{R}$$
4. $$v_e\propto \frac{1}{\sqrt{\rho} R}$$

Subtopic:  Escape velocity |
87%
From NCERT
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If a particle is dropped from a height $$h = 3R$$ from the Earth's surface, the speed with which the particle will strike the ground is:
1. $$\sqrt{3gR}$$
2. $$\sqrt{2gR}$$
3. $$\sqrt{1.5gR}$$
4. $$\sqrt{gR}$$

Subtopic:  Gravitational Potential Energy |
64%
From NCERT
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