A-Level AQA Physics Gravitational Fields: The Earth can be assumed to be a

The Earth can be assumed to be a uniform sphere of radius $R$ - AQA - A-Level Physics - Question 19 - 2018 - Paper 2

Question 19

The Earth can be assumed to be a uniform sphere of radius $R$. What is the mean density of the Earth?

Worked Solution & Example Answer:The Earth can be assumed to be a uniform sphere of radius $R$ - AQA - A-Level Physics - Question 19 - 2018 - Paper 2

Step 1

96%

114 rated

Answer

The mean density of a sphere can be calculated using the formula:

ho = \frac{M}{V}$$ where: - $ ho$ is the density, - $M$ is the mass, and - $V$ is the volume. For a uniform sphere, the mass $M$ can be expressed in terms of the gravitational constant $G$ and density: $$M = \rho V = \rho \left(\frac{4}{3} \pi R^3\right)$$ The volume of the sphere is given by: $$V = \frac{4}{3} \pi R^3$$ Substituting this into the density formula, we have: $$\rho = \frac{M}{\frac{4}{3} \pi R^3}$$ Given that the question requires the mean density using gravitational equations, we note: $$\rho = \frac{3g}{4\pi RG}$$ From the options provided, the mean density of the Earth corresponds to option D: $$\text{D: } \frac{3g}{4\pi RG}$$