Average density of the earth[AIEEE 2005]a)Does not depend on gb)Is a complex function of gc)Is directly proportional to gd)Is inversely proportional to gCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Answer

Answer

G=GM/R^2
g={Gp(4/3)πR^3}\R^2
g=4/3pπGR
[:.row (p)= density]
g is directly proportional to (p)density.

Answer

The average density of the Earth is directly proportional to the acceleration due to gravity (g). This means that as the value of g increases, the average density of the Earth also increases.

Explanation:
- Definition of average density: The average density of an object or a planet is defined as the total mass divided by the total volume. In the case of the Earth, we consider the mean density, which is the average density of the entire planet.
- Acceleration due to gravity (g): The acceleration due to gravity is a measure of the gravitational force acting on an object. It is the force that pulls objects towards the center of the Earth. The value of g varies depending on the location and altitude on Earth, but on average it is approximately 9.8 m/s^2.
- Relationship between density and gravity: The acceleration due to gravity depends on the mass and radius of the planet. The greater the mass and the smaller the radius, the stronger the gravitational force and hence the higher the value of g.
- Density and mass: The mass of an object is directly related to its density. If the mass of an object is high, it means that there is more material packed into a given volume, resulting in a higher density. In the case of the Earth, the greater the mass, the greater the average density.
- Density and volume: The volume of an object is indirectly related to its density. If the volume of an object is large, it means that the material is spread out over a larger space, resulting in a lower density. For the Earth, the volume remains constant, so as the mass (and therefore the density) increases, the acceleration due to gravity also increases.
- Density and gravitational force: The gravitational force acting on an object is directly proportional to its mass. Therefore, as the average density of the Earth increases, the gravitational force it exerts on objects also increases.

In conclusion, the average density of the Earth is directly proportional to the acceleration due to gravity (g). As the value of g increases, the mass and density of the Earth also increase.

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