Two particles of equal mass go round a circle of radius R under the action of their mutual

gravitational attraction. The speed of each particle is

1. ν=12R1Gm                             

2. ν=Gm2R

3. ν=12GmR                               

4. ν=4GmR   

Subtopic:  Newton's Law of Gravitation |
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The acceleration of a body due to the attraction of the earth (radius R) at a distance 2R

from the surface of the earth is (g = acceleration due to gravity at the surface of the

earth)

1. g9                       

2. g3

3. g4                       

4.  g

Subtopic:  Acceleration due to Gravity |
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 If V, R, and g denote respectively the escape velocity from the surface of the earth, the

radius of the earth, and acceleration due to gravity, then the correct equation is:

1. V=gR                                 

2. V=43gR3

3. V = Rg                                   

4. V=2gR

Subtopic:  Escape velocity |
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The depth at which the effective value of acceleration due to gravity is g4, is:

1. R                              

2. 3R4

3. R2                             

4. R4

Subtopic:  Acceleration due to Gravity |
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The value of \(g\) at a particular point is \(9.8~\text{m/s}^2\). Suppose the earth suddenly shrinks uniformly to half its present size without losing any mass then value of \(g\) at the same point will now become: (assuming that the distance of the point from the centre of the earth does not shrink)

1. \(4.9~\text{m/s}^2\) 2. \(3.1~\text{m/s}^2\)
3. \(9.8~\text{m/s}^2\) 4. \(19.6~\text{m/s}^2\)
Subtopic:  Acceleration due to Gravity |
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If both the mass and the radius of the earth is decreased by \(1\%\), then the value of the acceleration due to gravity will:
1. decrease by \(1\%\) 2. increase by \(1\%\)
3. increase by \(2\%\) 4. remain unchanged
Subtopic:  Acceleration due to Gravity |
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The earth (mass = 6×1024kg ) revolves round the sun with angular velocity

2×107rad/s in a circular orbit of radius 1.5×108km . The force exerted by the sun on

the earth in Newtons, is

1. 18×1025                               

2. Zero

3. 27×1039                               

4. 36×1021

Subtopic:  Newton's Law of Gravitation |
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The gravitational force between two point masses m1  and m2  at separation r is given by F=km1m2r2  The constant k                                                                

1. Depends on system of units only

2. Depends on medium between masses only

3. Depends on both 1 and 2

4. Is independent of both 1 and 2

Subtopic:  Newton's Law of Gravitation |
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The density of a newly discovered planet is twice that of earth. The acceleration due to

gravity at the surface of the planet is equal to that at the surface of the earth. If the

radius of the earth is R, the radius of the planet would be

1. 2R                   

2. 4R

3. 14R               

4. 12R     

Subtopic:  Acceleration due to Gravity |
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If R is the radius of the earth and g the acceleration due to gravity on the earth's surface,

the mean density of the earth is:

1. 4πG/3gR                                 

2. 3πR/4gG

3. 3g/4πRG                               

4.πRG/12G        

Subtopic:  Acceleration due to Gravity |
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