Question

A regular cylinder of height 10.0 cm is placed in water so that 5.00 cm of its height are underwater. Given the density of water is 1 gram/cm^3. What is the density of this cylinder? A)10.0 grams/cm^3 B)0.500 gram/cm^3 C)57.9 grams/cm^3 D)131 grams/cm^3 E)200 grams/cm^3

Answer 1

When an object floats in a liquid, the ratio between the submerged volume and the total volume of the object is the same as the ratio between the density of the object and the density of the liquid:

`\frac{V_{\text{submerged}}}{V_{\text{total}}}=\frac{\rho_{\text{object}}}{\rho_{\text{liquid}}}_{}`

Since the cylinder floats with half of its volume submerged, then:

`\frac{V_{\text{submerged}}}{V_{\text{total}}}=(1)/(2)`

Then:

`\begin{gathered} \frac{\rho_{\text{object}}}{\rho_{\text{water}}}=(1)/(2) \\ \Rightarrow\rho_(object)=(1)/(2)\rho_(water) \end{gathered}`

Since the density of water is 1 gram per cubic centimeter, then:

`\rho_{\text{object}}=(1)/(2)(1(g)/(cm^3))=0.5(g)/(cm^3)`

Therefore, the correct choice is option B) 0.500 gram/cm^3.