A sphere of radius r is made from material of density $\rho_{s}$ - Edexcel - A-Level Physics - Question 1 - 2023 - Paper 2

To determine the uplift (or buoyant force) on the sphere, we apply Archimedes' principle, which states that the buoyant force equals the weight of the liquid displaced by the submerged object.

The volume of the sphere can be calculated using the formula: $V = \frac{4}{3} \pi r^{3}$

The upward buoyant force is then given by the weight of the fluid displaced: $F_{b} = V \cdot \rho_{l} \, g = \frac{4}{3} \pi r^{3} \rho_{l} \, g$

Thus, the correct expression that gives the uplift on the sphere is option C: $F_{b} = \frac{4}{3} \pi r^{3} \rho_{l} g$