Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

What are the conditions that would cause said sphere to sink or float?

What if the sphere was full of ice instead?

share|cite|improve this question
up vote 5 down vote accepted

Simply if the average density $\rho_\text{avg}$ of the sphere + helium (or your horse, for that matter) is less than the density of water $\rho_w$.

This is because the weight is \begin{align} mg = \rho_\text{avg} V_\text{object} g \end{align} while the buoyancy force is \begin{align} F = \rho_w V_\text{displaced} g, \end{align} where $V_\text{object}$ is the volume of the object and $V_\text{displaced}$ is the volume of water displaced i.e. the volume of the object under water. Of course, $V_\text{object} \geq V_\text{displaced}$, because you can only displace as much volume of water as the volume you take up anyway.

If $\rho_\text{avg} \leq \rho_w$ then there exists some $V_\text{displaced}$ which is $ \leq V_\text{object}$ that satisfies $F = mg$, so the object floats, with a bit of it sticking out of the water, and if $\rho_\text{avg} > \rho_w$ then it just sinks and sinks and sinks...


share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.