A uniform cylinder of wood of length 25 cm is floating vertically upright in a dual layered fluid.An oil layer (of density 0.9 g/cm³)that is 9 cm deep lies above a depth of water.If only 5 cm of wood lies above the oil surface calculate the density of the wood. A)0.76 g/ cm³ B)0.80 g/ cm³ C)0.70 g/ cm³ D)0.66 g/ cm³ E)none of the above

Question

Quizplus · Accepted Answer

We can use the principle of buoyancy to solve this problem. The buoyant force acting on the cylinder is equal to the weight of the fluid displaced by the cylinder. Let V be the volume of the cylinder, h1 be the height of the oil layer (9 cm), h2 be the height of the water layer (unknown), and d be the density of the wood (unknown). Then, we have:

Buoyant force = Weight of fluid displaced
dVg = (0.9)(Vh1)g + (1)(Vh2)g
d = (0.9h1 + h2)

Now, we can use the fact that only 5 cm of the cylinder is above the oil surface to find h2:

25 cm - 9 cm - 5 cm = 11 cm

Therefore, h2 = 11 cm. Substituting into the previous equation, we get:

d = (0.9)(9 cm) + (11 cm)
d = 8.1 cm + 11 cm
d = 19.1 cm

Finally, we convert cm to g/cm^3:

d = 0.76 g/cm^3

Thus, the answer is choice A.

A Uniform Cylinder of Wood of Length 25 Cm Is