When we say that the weight of an object is Mg, and that g = 9.8 N/kg, what assumptions are we making?

Which of the below?

The distribution of mass in the earth is spherically symmetric.
The density of the earth is the same everywhere.
The earth's interior is solid everywhere.
The orbit of the earth is circular and not elliptical.
We neglect the effect of astronomical bodies other than the earth.
The object is at the earth's surface.
Two significant figures are sufficient.
Newton's law of gravitation holds.

When we say that the weight of an object is Mg, and that g = 9.8 N/kg, we are making several assumptions. Let's go through each option and determine which assumptions are being made:

1. The distribution of mass in the earth is spherically symmetric: This assumption means that the mass of the Earth is uniformly distributed in all directions, which allows us to simplify the gravitational calculations. While this assumption is often used for simplicity, it is not entirely accurate as the mass distribution of the Earth is not perfectly spherically symmetric. However, for many practical purposes, this assumption is reasonable.

2. The density of the Earth is the same everywhere: This assumption assumes a homogeneous distribution of Earth's mass, implying that the density remains constant from the surface to the core. In reality, the density of the Earth does vary with depth, but for basic calculations, assuming a constant density is a reasonable approximation.

3. The Earth's interior is solid everywhere: This assumption is not directly related to the weight calculation. It refers to the assumption that the Earth's interior is a solid rather than being layered or having distinct regions.

4. The orbit of the Earth is circular and not elliptical: This assumption is unrelated to the weight calculation and refers to the shape of the Earth's orbit around the Sun. For the purpose of calculating weight, the shape of Earth's orbit is not relevant.

5. We neglect the effect of astronomical bodies other than the Earth: This assumption means that we consider the gravitational influence of other celestial bodies, such as the Moon or other planets, as negligible. While this assumption is valid for calculating the weight of an object on Earth, it may not hold in more precise calculations.

6. The object is at the Earth's surface: This assumption assumes that the object's height above the Earth's surface is negligible compared to the Earth's radius. As a result, we can disregard any variations in the strength of gravity with height. The weight calculation will be most accurate when the object is close to the Earth's surface.

7. Two significant figures are sufficient: This assumption indicates that the values used in calculations are rounded to two significant figures. This assumption simplifies the calculations while still providing a reasonably accurate estimate. However, for more precise calculations, additional significant figures may be necessary.

8. Newton's law of gravitation holds: This assumption is fundamental for calculating weight. Newton's law of gravitation states that the force of gravity acting on an object is proportional to the mass of the object and inversely proportional to the square of the distance between the objects. For weight calculations, this assumption is valid and widely accepted.

In summary, the assumptions made when stating that the weight of an object is Mg, and that g = 9.8 N/kg, include assuming a spherically symmetric mass distribution in the Earth, assuming a constant density throughout the Earth, neglecting the effects of other astronomical bodies, assuming the object is at the Earth's surface, assuming two significant figures are sufficient, and assuming Newton's law of gravitation holds.