The time period of a geostationary satellite is \(24~\text{h}\) at a height \(6R_E\) \((R_E\) is the radius of the earth) from the surface of the earth. The time period of another satellite whose height is \(2.5R_E\) from the surface will be:
1. \(6\sqrt{2}~\text{h}\)
2. \(12\sqrt{2}~\text{h}\)
3. \(\frac{24}{2.5}~\text{h}\)
4. \(\frac{12}{2.5}~\text{h}\)

Subtopic:  Kepler's Laws |
 65%
From NCERT
NEET - 2019
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Assuming that the gravitational potential energy of an object at infinity is zero, the change in potential energy (final - initial) of an object of mass \(m\) when taken to a height \(h\) from the surface of the earth (of radius \(R\) and mass \(M\)), is given by:
1. \(-\frac{GMm}{R+h}\)
2. \(\frac{GMmh}{R(R+h)}\)
3. \(mgh\)
4. \(\frac{GMm}{R+h}\)

Subtopic:  Gravitational Potential Energy |
 62%
From NCERT
NEET - 2019
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A mass falls from a height '\(h\)' and its time of fall '\(t\)' is recorded in terms of time period \(T\) of a simple pendulum. On the surface of the earth, it is found that \(t=2T\). The entire setup is taken on the surface of another planet whose mass is half of that of the Earth and whose radius is the same. The same experiment is repeated and corresponding times are noted as '\(t\)' and '\(T\)'. Then we can say:
1. \(t' = \sqrt{2}T\)
2. \(t'>2T'\)
3. \(t'<2T'\)
4. \(t' = 2T'\)

Subtopic:  Acceleration due to Gravity |
From NCERT
NEET - 2019
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A uniform spherical shell gradually shrinks maintaining its shape. The gravitational potential at the centre:

1. increases

2. decreases

3. remains constant

4. oscillates

Subtopic:  Gravitational Potential |
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Which of the following graphs represents correctly the variation of intensity of gravitational field l with the distance r from the centre of a spherical shell of mass M and radius a?

1. 

2. 

3. 

4. 

Subtopic:  Gravitational Field |
 74%
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A particle of mass M is at distance 'a' from the surface of a thin spherical shell of mass M and radius a. If Vo and Vs are the potentials at the centre and the surface of the shell respectively, then

1. VS>VO

2. VS<VO

3. VS=VO

4. Can't say

 

Subtopic:  Gravitational Potential |
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The distance between the centres of moon and earth is D. The mass of earth is 81 times the mass of the moon. At what distance from the centre of the earth the gravitational force will be zero ?

1. D2                                2. 2D2                                

3. 4D3                              4. 9D10

Subtopic:  Gravitational Field |
 79%
From NCERT
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Which one of the following plots represent

the variation of gravitational field on a 

particle at distance r, due to a thin 

spherical shell of radius R? (r is measured 

from the centre of the spherical shell).

1.  2.

3.    4. 

Subtopic:  Gravitational Field |
 73%
From NCERT
NEET - 2012
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A planet whose density is double of earth and radius is half of the earth, will produce gravitational field on its
surface:(\(g=\) acceleration due to gravity at the surface of earth)
1. \(g\)
2. \(2g\)
3. \(\frac{g}{2}\)
4. \(3g\)

Subtopic:  Gravitational Field |
 78%
From NCERT
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Potential energy (U) and time period (T) of a satellite are related to each other as

1.  T2  1U3

2.  T  1U3

3.  T2  U3

4.  U2  1T3

Subtopic:  Kepler's Laws |
 70%
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