Question

Acceleration due to gravity is .................... proportional to the density of the planet​

Answer 1

Answer:

Acceleration due to gravity is proportional to mean density of earth, and its radius.

Acceleration due to gravity g is given by GM/r^2, where G is the universal gravitational constant, M is the mass of earth and r is the distance between the centre of mass earth and the center of mass of the object, which can be safely assumed to be equal to the radius of earth.

From the above correlation we can say g is proportional to mass of the earth and independent of the mass of the object, as its size (volume) is negligible compared to earth, another assumption. So, it is evident that the density (mass per unit volume) of the object has no role in determining g under normal earthly conditions. In case of density of earth, which is nonuniform, it does not concern us as we have assumed the centre of mass of earth for our calculations.

Thus, in case of earth and daily life situations, acceleration due to gravity g is independent of density.

Answer 2

Answer:

Acceleration due to gravity g is given by GM/r^2, where G is the universal gravitational constant, M is the mass of earth and r is the distance between the centre of mass earth and the center of mass of the object, which can be safely assumed to be equal to the radius of earth