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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Radius of orbit of satellite of earth is R. Its kinetic energy is proportional to -

1. 1R                      

2. 1R

3. R                         

4.  1R3/2

Subtopic:  Gravitational Potential Energy | Satellite |
 78%
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A particle falls towards earth from infinity. It’s velocity on reaching the earth would be -

(1)   Infinity                   

(2) 2gR

(3)   2gR                   

(4)  Zero

Subtopic:  Escape velocity |
 81%
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