Solution Found!
A homogeneous solid object floats on water, with 80.0
Chapter , Problem 45(choose chapter or problem)
A homogeneous solid object floats on water, with 80.0 percent of its volume below the surface. When placed in a second liquid, the same object floats on that liquid with 72.0 percent of its volume below the surface. Determine the density of the object and the specific gravity of the liquid.
Questions & Answers
QUESTION:
A homogeneous solid object floats on water, with 80.0 percent of its volume below the surface. When placed in a second liquid, the same object floats on that liquid with 72.0 percent of its volume below the surface. Determine the density of the object and the specific gravity of the liquid.
ANSWER:Step 1 of 2:
Considering the Archimedes Principle:
Buoyant force on an object is equal to the weight of the water/liquid displaced by the object, hence
\(F_{b}=W\)
\(\rho_{w} V_{\text {displaced }} g=\rho_{\text {object }} V_{\text {object }} g\)
Since the object is submerged 80% in water,
\(V_{\text {displaced }}=0.8 V_{\text {object }}\)
\(r h o_{w}(0.8)=\rho_{\text {object }}\) ........................................(1)
Density of water is \(1000 \mathrm{~kg} / \mathrm{m}^{3}\)
\(1000 \times 0.8=\rho_{\text {object }}\).
\(\rho_{\text {object }}=800 \mathrm{~kg} / \mathrm{m}^{3}\)