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If the acceleration due to gravity inside the earth is to be kept constant, then the relation between the density d and the distance r from the centre of earth will be -
- a)d µ r
- b)d µ r1/2
- c)d µ 1/r
- d)d µ
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If the acceleration due to gravity inside the earth is to be kept cons...
If M is the mass of the Earth and m is the mass of a sphere of radius r and you want the force of gravity to be the same at both the surface of the sphere and the surface of the earth then mg = Mg and m = M. This means that the mass of the sphere would have to be the same as the mass of the Earth no matter what r is. This is impossible since a sub-sphere cannot have the same mass as its parent.
For a sphere of radius r to have force g at its surface, d = (De *Re)/r where De is the density of the entire Earth and Re is the radius of the Earth, d is the density of the sphere of radius r. So there is a radius and a density which will produce a gravitational force of g for any d, r >0 but one cannot be a subset of another.
For a sphere of radius r to have force g at its surface, d = (De *Re)/r where De is the density of the entire Earth and Re is the radius of the Earth, d is the density of the sphere of radius r. So there is a radius and a density which will produce a gravitational force of g for any d, r >0 but one cannot be a subset of another.
= d μ 1/rMost Upvoted Answer
If the acceleration due to gravity inside the earth is to be kept cons...
If M is the mass of the Earth and m is the mass of a sphere of radius r and you want the force of gravity to be the same at both the surface of the sphere and the surface of the earth then mg=Mg and m=M. This means that the mass of the sphere would have to be the same as the mass of the Earth no matter what r is. This is impossible since a sub-sphere cannot have the same mass as its parent.
for a sphere of radius r to have force g at its surface, d= (De *Re)/r
where De is the density of the entire Earth and Re is the radius of the Earth, d is the density of the sphere of radius r. So there is a radius and a density which will produce a gravitational force of g for any d,r >0 but one cannot be a subset of another.
for a sphere of radius r to have force g at its surface, d= (De *Re)/r
where De is the density of the entire Earth and Re is the radius of the Earth, d is the density of the sphere of radius r. So there is a radius and a density which will produce a gravitational force of g for any d,r >0 but one cannot be a subset of another.
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If the acceleration due to gravity inside the earth is to be kept cons...
If M is the mass of the Earth and m is the mass of a sphere of radius r and you want the force of gravity to be the same at both the surface of the sphere and the surface of the earth then mg = Mg and m = M. This means that the mass of the sphere would have to be the same as the mass of the Earth no matter what r is. This is impossible since a sub-sphere cannot have the same mass as its parent.
For a sphere of radius r to have force g at its surface, d = (De *Re)/r where De is the density of the entire Earth and Re is the radius of the Earth, d is the density of the sphere of radius r. So there is a radius and a density which will produce a gravitational force of g for any d, r >0 but one cannot be a subset of another.
For a sphere of radius r to have force g at its surface, d = (De *Re)/r where De is the density of the entire Earth and Re is the radius of the Earth, d is the density of the sphere of radius r. So there is a radius and a density which will produce a gravitational force of g for any d, r >0 but one cannot be a subset of another.
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If the acceleration due to gravity inside the earth is to be kept constant, then the relation between the density d and the distance r from the centre of earth will be -a)d µ rb)d µ r1/2c)d µ 1/rd)d µCorrect answer is option 'C'. Can you explain this answer?
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