The gravitational field due to a mass distribution is E=K/x3 in the x-direction. (K is a

constant). Taking the gravitational potential to be zero at infinity, its value at a distance x

is

1. K/x                    

2. K/2x

3. K/x2                 

4. K/2x2

Subtopic:  Gravitational Potential |
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The change in the potential energy, when a body of mass \(m\) is raised to a height \(nR\) from the Earth's surface is: (\(R\) = Radius of the Earth)
1. \(mgR\left(\frac{n}{n-1}\right)\)
2. \(nmgR\)
3. \(mgR\left(\frac{n^2}{n^2+1}\right)\)
4. \(mgR\left(\frac{n}{n+1}\right)\)

Subtopic:  Gravitational Potential Energy |
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The value of g on the earth's surface is 980 cm/sec2 . Its value at a height of 64 km from

the earth's surface is

1.   960.40 cm/sec2       

2.   984.90 cm/sec2

3.   982.45 cm/sec2         

4. 980.45 cm/sec2

(Radius of the earth R = 6400 kilometers)     

Subtopic:  Acceleration due to Gravity |
 72%
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If the earth suddenly shrinks (without changing mass) to half of its present radius, the acceleration due to gravity will be:

1. g/2                             

2. 4g

3. g/4                            

4. 2g

Subtopic:  Acceleration due to Gravity |
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The masses and radii of the earth and moon are M1, R1 and M2, R2 respectively. Their centres are distance d apart. The minimum velocity with which a particle of mass should be projected from a point midway between their centres so that it escapes to infinity is:

1. 2GDM1+M2                 

2. 22GD(M1+M2)

3. 2GMDM1+M2               

4. 2GMM1+M2DR1+R2

Subtopic:  Gravitational Potential Energy |
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If the mass of the earth is M, the radius is R and the gravitational constant is G, then work done to take

1 kg mass from earth surface to infinity will be:

1.  GM2R                      

2.  GMR

3.   2GMR                

4.   GM2R

Subtopic:  Gravitational Potential Energy |
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If ve and vo represent the escape velocity and orbital velocity of a satellite corresponding

to a circular orbit of radius R, then 

1. ve=vo                     

2. 2vo=ve

3. ve=vo/2               

4. ve and vo are not related

Subtopic:  Escape velocity | Orbital velocity |
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If r represents the radius of the orbit of a satellite of mass m moving around a planet of

mass M, the velocity of the satellite is given by: 

1. v2=gMr                     

2. v2=GMmr

3. v=GMr                        

4. v2=GMr

Subtopic:  Satellite |
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An earth satellite of mass m revolves in a circular orbit at a height h from the surface of

the earth. R is the radius of the earth and g is acceleration due to gravity at the surface

of the earth. The velocity of the satellite in the orbit is given by:

1. gR2R+h                     

2. gR

3. gRR+h                     

4. gR2R+h

Subtopic:  Orbital velocity |
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A satellite which is geostationary in a particular orbit is taken to another orbit. Its

distance from the centre of earth in new orbit is 2 times that of the earlier orbit. The time

period in the second orbit is:

1. 4.8 hours                         

2. 482 hours

3. 24 hours                           

4. 242 hours

Subtopic:  Satellite |
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