Let g be the acceleration due to gravity at earth's surface and K be the rotational kinetic energy of the earth. Suppose the earth's radius decreases by 2% keeping all other quantities same, then

(1)  g decreases by 2% and K decreases by 4%

(2)  g decreases by 4% and K increases by 2%

(3)  g increases by 4% and K increases by 4%

(4)  g decreases by 4% and K increases by 4%

Subtopic:  Acceleration due to Gravity |
 72%
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The distance between centre of the earth and moon is 384000 km. If the mass of the earth is 6×1024 kg and G=6.66×10-11 Nm2/kg2 . The speed of the moon is nearly -

(a) 1 km/sec                          (b) 4 km/sec

(c) 8 km/sec                          (d) 11.2 km/sec

Subtopic:  Orbital velocity |
 50%
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A body is projected vertically upwards from the surface of a planet of radius \(R\) with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is:
1. \(\frac{R}{3}\)
2. \(\frac{R}{2}\)
3. \(\frac{R}{4}\)
4. \(\frac{R}{5}\)

Subtopic:  Escape velocity |
 64%
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A satellite is launched into a circular orbit of radius \(R\) around the Earth while a second satellite is launched into an orbit of radius \(1.02~\text{R}\). The percentage difference in the time periods of the two satellites is: 

1. \(0.7\) 2. \(1.0\)
3. \(1.5\) 4. \(3\)
Subtopic:  Kepler's Laws |
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Distance of geostationary satellite from the center of the Earth  (Re=6400 km) in terms of Re is-

(1) 13.76 Re                        

(2) 10.76 Re

(3) 6.59 Re                            

(4) 2.56 Re

Subtopic:  Satellite |
 70%
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Energy required to move a body of mass m from an orbit of radius 2R to 3R is

(1)    GMm/12R2               

(2)    GMm/3R2

(3)     GMm/8R                 

(4)     GMm/6R

Subtopic:  Gravitational Potential Energy |
 71%
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If the radius of the earth contracts by 2% and its mass remains the same, then weight of the body at the earth surface :

(1)  Will decrease                      

(2)  Will increase

(3)   Will remain the same             

(4)  None of these

Subtopic:  Acceleration due to Gravity |
 78%
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The kinetic energy needed to project a body of mass m from the earth surface (radius R) to infinity is -

(1)   mgR/2                 

(2)  2 mgR

(3)   mgR                   

(4)   mgR/4

Subtopic:  Escape velocity |
 66%
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A satellite is to revolve round the earth in a circle of radius 8000 km. The speed at which this satellite be projected into an orbit, will be 
(1) 3 km/s                     

(2) 16 km/s

(3) 7.15 km/s                   

(4) 8 km/s

Subtopic:  Satellite |
 55%
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If the mass of a body is M on the earth surface, then the mass of the same body on the moon surface is:

(1)  M/6       

(2)  Zero

(3)  M          (4)   None of these

Subtopic:  Acceleration due to Gravity |
 67%
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