Forces, Density and Pressure: Question 5

Worked solution

Setting up the problem

Archimedes’ principle states that the upthrust on a submerged object equals the weight of fluid it displaces: $F = \rho g V$ where $\rho$ is the density of the fluid, $V$ is the volume of fluid displaced (here, the full volume of the sphere, since it is fully submerged), and $g$ is the acceleration of free fall.

Calculating the upthrust

$F = \rho g V = (1000)(9.81)(2.0\times10^{-4})$ $F = 9810 \times 2.0\times10^{-4}$ $F = 1.962\text{ N} \approx 1.96\text{ N}$

Why the other options are wrong

• A ($0.20\text{ N}$): this omits $g$ entirely, i.e. calculates $\rho V$ instead of $\rho g V$.
• C ($2.00\text{ N}$): this uses $g = 10\text{ m s}^{-2}$ instead of the given value $g = 9.81\text{ m s}^{-2}$.
• D ($19.6\text{ N}$): this is ten times too large, from a decimal/power-of-ten slip in the volume (e.g. using $2.0\times10^{-3}\text{ m}^3$ instead of $2.0\times10^{-4}\text{ m}^3$).

Final answer

• Upthrust on the sphere $= \boxed{1.96}\text{ N}$, option B.