A sphere of radius r is made from material of density ρₘ - Edexcel - A-Level Physics - Question 1 - 2023 - Paper 2

The uplift, or buoyant force, acting on a body submerged in a fluid can be determined using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the body.

The volume V of a sphere is given by the formula:

$V = \frac{4}{3} \pi r^3$

The buoyant force F_b can be calculated as:

$F_b = \text{Weight of the fluid displaced} = \rho_l \cdot V imes g = \rho_l \cdot \left(\frac{4}{3} \pi r^3\right) \cdot g$

The expression for the uplift on the sphere is:

$F_b = \frac{4}{3} \pi r^3 \rho_l g$

Thus, the correct answer corresponds to option C.