Answer to Question #181530 in Physics for Kise

Question

A simple compass can be made by placing a small iron bar magnet on a cork floating in the water. If the cork has a mass of 12.2 g and a 20-g magnet is placed on it, what fraction of the cork will be submerged?

Round your answer to 3 decimal places

Answer 1

The cork will float when the buoyancy force is equal to the force of gravity:

$$\rho_\text{water} g(V·k)=g(m+M)\\\space\\ V=\frac{m}{\rho_\text{cork}}\\\space\\ \rho_\text{water} g\frac{m}{\rho_\text{cork}}k=g(m+M),\\\space\\ k=\frac{(m+M)\rho_\text{cork}}{m\rho_\text{water}}=0.633.$$