Question

A frog in a hemispherical bowl, as shown below, just floats in a fluid with a density of 1.29 103 kg/m3. If the bowl has a radius of 5.36 cm and negligible mass, what is the mass of the frog?

Answer 1

Question 22284

If bowl floats in fluid (and we neglect its mass), the buoyant force is compensated by the gravitational force, which acts on the frog. The following equation expresses the latter thought:

$$m_f \cdot g = V_{\text{bowl}} \cdot \rho \cdot g,$$

where $m_f$ is the mass of the frog, $V_{\text{bowl}}$ is the volume of the hemispherical bowl, $\rho = 1.29 \cdot 10^3 \, \text{kg/m}^3$ is the density of the fluid.

Knowing that the volume of the hemisphere is $V_{\text{bowl}} = \frac{1}{2} V_{\text{sphere}} = \frac{2}{3} \pi r^3$, and plugging this expression into first equation, obtain: $m_f = V_{\text{bowl}} \rho = \frac{2}{3} \pi r^3 \rho = 0.42 \, \text{kg}$.