Question

Logs sometimes float vertically in a lake because one end has become water-logged and denser than the other. What is the average density of a uniform-diameter log that floats with 20.0% of its length above water?

a.Average Density=0.80×Density of Water
b. Average Density=1.25×Density of Wate
c. Average Density=0.20×Density of Water
d. Average Density=5.00×Density of Water

Answer 1

The average density of a log floating with 80% of its volume submerged in water is equal to 0.80 times the density of water because Archimedes' Principle states that the buoyant force equals the weight of the displaced fluid.

Step-by-step explanation:

When a log floats vertically in a lake, with 20% of its length above water, it means that 80% of the log's volume is submerged and displacing water. According to Archimedes' Principle, the weight of the water displaced by the submerged part of the log equals the weight of the log itself. Since the density is mass per unit volume and the log floats stably, the average density of the log must be equal to the density of the water multiplied by the fraction that is submerged. Therefore, if the density of water is considered to be 1, the average density of the log is 0.80 times the density of water.