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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The kinetic energies of a planet in an elliptical orbit around the Sun, at positions \(A,B~\text{and}~C\) are \(K_A, K_B~\text{and}~K_C\) respectively. \(AC\) is the major axis and \(SB\) is perpendicular to \(AC\) at the position of the Sun \(S\), as shown in the figure. Then:
                 

1. \(K_A <K_B< K_C\) 2. \(K_A >K_B> K_C\)
3. \(K_B <K_A< K_C\) 4. \(K_B >K_A> K_C\)
Subtopic:  Kepler's Laws |
 76%
From NCERT
NEET - 2018
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At what height from the surface of the earth, the gravitation potential and the value of \(g\) are: \(-5.4 \times 10^7\) Jkg-2 and \(6.0~\text{ms}^{-2}\) respectively? (Take, the radius of earth as \(6400\) km.)
1. \(1600\) km
2. \(1400\) km
3. \(2000\) km
4. \(2600\) km
Subtopic:  Gravitational Potential |
 67%
From NCERT
NEET - 2016
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The ratio of escape velocity at earth \((v_e)\) to the escape velocity at a planet \((v_p)\) whose radius and mean density are twice that of the earth is:
1. \(1:2\sqrt{2}\)
2. \(1:4\)
3. \(1:\sqrt{2}\)
4. \(1:2\)
Subtopic:  Escape velocity |
 70%
From NCERT
NEET - 2016
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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 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 |
 63%
From NCERT
AIPMT - 2014
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