The mean radius of the earth is R, its angular speed on its own axis is ω and the acceleration due to gravity at the earth's surface is g. The cube of the radius of the orbit of a geostationary satellite will be -

(1) R2g/ω                   

(2) R2ω2/g

(3) Rg/ω2                    

(4) R2g/ω2

Subtopic:  Orbital velocity |
 58%
From NCERT
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A satellite whose mass is m, is revolving in a circular orbit of radius r, around the earth of mass M. Time of revolution of the satellite is:

1. Tr5GM

2. Tr3GM

3. TrGM2/3

4. Tr3GM2/4

Subtopic:  Kepler's Laws |
 81%
From NCERT
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Suppose the gravitational force varies inversely as the nth power of distance then the time period of a planet in circular orbit of radius R around the sun will be proportional to:

1. Rn+12                 

2. Rn-12

3. Rn                         

4. Rn-22  

Subtopic:  Newton's Law of Gravitation |
 64%
From NCERT
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The orbital speed of an artificial satellite very close to the surface of the earth is Vo. Then the orbital speed of another artificial satellite at a height equal to three times the radius of the earth is 

(a) 4 V0                    (b) 2 V0

(c) 0.5V0                   (d) 4 V0

Subtopic:  Orbital velocity |
 75%
From NCERT
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The distance of a geostationary satellite from the centre of the earth (Radius R = 6400 km) is nearest to:

(1) 5R                                     (2) 7R

(3) 10R                                   (4) 18R

Subtopic:  Satellite |
 70%
From NCERT
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In order to make the effective acceleration due to gravity equal to zero at the equator, the angular velocity of rotation of the earth about its axis should be (g=10 ms-2 and radius of earth is 6400 kms)

(1) 0 rad/sec                   

(2) 1800 rad/sec

(3) 180 rad/sec               

(4) 18 rad/sec

Subtopic:  Acceleration due to Gravity |
 71%
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A body of mass \(m\) is taken from the earth's surface to the height \(h\) equal to the radius of the earth, the increase in potential energy will be:
1. \(mgR\)
2. \(\frac{1}{2}~mgR\)
3. \(2 ~mgR\)
4. \(\frac{1}{4}~mgR\)

Subtopic:  Gravitational Potential Energy |
 81%
From NCERT
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Time period of a satellite revolving above Earth’s surface at a height equal to \(\mathrm{R}\) (the radius of Earth) will be:
(g is the acceleration due to gravity at Earth’s surface)

1. 2π2Rg

2. 42πRg

3. 2πRg

4. 8πRg 

Subtopic:  Satellite |
From NCERT
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An artificial satellite moving in a circular orbit around the earth has a total (kinetic + potential) energy E0 . Its potential energy is:

(1) -E0                       

(2) 1.5 E0

(3) 2E0                         

(4) E0

Subtopic:  Gravitational Potential Energy |
 78%
From NCERT
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Given the radius of Earth ‘R’ and length of a day ‘T’, the height of a geostationary satellite is:

[G–Gravitational Constant, M–Mass of Earth] 

(a) 4π2GMT213                      (b) 4πGMR213-R

(c) GMT24π213-R                   (d) GMT24π213+R

Subtopic:  Kepler's Laws |
 66%
From NCERT
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