An object displaces \(3.0\times10^{-4}\,\mathrm{m^3}\) of water. Find the buoyant force.

A buoyant force of \(12\,\mathrm{N}\) acts on an object in oil of density \(800\,\mathrm{kg\,m^{-3}}\). Find the displaced volume.

A body weighs \(45\,\mathrm{N}\) in air and displaces \(2.5\times10^{-3}\,\mathrm{m^3}\) of water when fully immersed. Find the supporting force reading while it is immersed.

A uniform object of density \(600\,\mathrm{kg\,m^{-3}}\) floats in water. What fraction of its volume is submerged?

A floating block has mass \(1.8\,\mathrm{kg}\). Find the volume of water it displaces.

An object floats in freshwater with \(72\%\) of its volume submerged. Find its average density.

The same fully submerged object is placed first in water and then in a liquid of density \(1260\,\mathrm{kg\,m^{-3}}\). Compare the buoyant forces.

A solid object has volume \(1.2\times10^{-3}\,\mathrm{m^3}\) and density \(2700\,\mathrm{kg\,m^{-3}}\). Find its apparent weight while fully submerged in water.

An object weighs \(18\,\mathrm{N}\) in air and \(11\,\mathrm{N}\) when fully submerged in water. Find its volume and average density.

A cube of side \(0.20\,\mathrm{m}\) and density \(750\,\mathrm{kg\,m^{-3}}\) floats upright in water. Find the submerged height.

A vertical floating cylinder has cross-sectional area \(0.030\,\mathrm{m^2}\) and mass \(18\,\mathrm{kg}\). Find its submerged depth in water.

A sealed raft has volume \(0.60\,\mathrm{m^3}\) and mass \(180\,\mathrm{kg}\). Find the maximum extra mass it can carry in water before it is just fully submerged.

A fully submerged object has volume \(1.0\times10^{-2}\,\mathrm{m^3}\) and weight \(70\,\mathrm{N}\). It is tethered underwater in water. Find the tether force and its direction on the object.

A solid of volume \(4.0\times10^{-3}\,\mathrm{m^3}\) and density \(1200\,\mathrm{kg\,m^{-3}}\) is held fully submerged in oil of density \(850\,\mathrm{kg\,m^{-3}}\). Find the string tension needed for equilibrium and its direction on the solid.

A uniform block of density \(900\,\mathrm{kg\,m^{-3}}\) floats at the interface between oil \((800\,\mathrm{kg\,m^{-3}})\) above and water \((1000\,\mathrm{kg\,m^{-3}})\) below. If the block has vertical height \(H\), find the fraction of its height in water.

A hydrometer of mass \(0.020\,\mathrm{kg}\) has a narrow vertical stem of cross-sectional area \(1.0\times10^{-4}\,\mathrm{m^2}\). It floats first in water and then in a liquid of density \(800\,\mathrm{kg\,m^{-3}}\). Find how much farther the stem sinks in the lower-density liquid.

A composite floating body is made from foam of volume \(0.030\,\mathrm{m^3}\) and density \(120\,\mathrm{kg\,m^{-3}}\), plus a metal insert of volume \(0.0020\,\mathrm{m^3}\) and density \(7800\,\mathrm{kg\,m^{-3}}\). Determine whether it floats in water and, if so, what fraction of its total volume is submerged.

A wooden float of volume \(0.040\,\mathrm{m^3}\) and density \(550\,\mathrm{kg\,m^{-3}}\) has a dense metal piece of density \(7800\,\mathrm{kg\,m^{-3}}\) attached to it. Derive and calculate the maximum metal volume before the combination just sinks in water.

A vertical cylinder of cross-sectional area \(A\) and height \(H\) is fully submerged from depth \(y=a\) to \(y=a+H\) in a fluid with density \(\rho(y)=\rho_0(1+\beta y)\). Derive the buoyant force.

A uniform object floats in a liquid inside an elevator accelerating upward with acceleration \(a\). Using an effective gravitational field \(g+a\), show whether the submerged fraction changes compared with the elevator at rest. State the assumptions.