A rectangular wooden block measures 10.0 cm × 4.00 cm × 2.00 cm.When the block is placed in water,it floats horizontally,with its bottom face 1.65 cm below the surface.What is the density of the wood? A)0.825 g/cm³ B)1.21 g/cm³ C)1.65 g/cm³ D)0.606 g/cm³ E)0.350 g/cm³

Question

Quizplus · Accepted Answer

The buoyant force acting on the block is equal to the weight of the water displaced by the block. Since the block floats with its bottom face 1.65 cm below the surface, we know that the volume of water displaced is equal to the volume of the block below the waterline.

Volume of water displaced = (10.0 cm)(4.00 cm)(1.65 cm) = 66.0 cm^3

The mass of the water displaced is equal to its volume times its density, which is 1.00 g/cm^3.

Mass of water displaced = (66.0 cm^3)(1.00 g/cm^3) = 66.0 g

Since the block is floating, the buoyant force equals the weight of the block:

Buoyant force = weight of block

Density of block x volume below waterline x g = density of water x volume of water displaced x g

Solving for the density of the block:

Density of block = (density of water) x (volume of water displaced) / (volume below waterline)

Density of block = (1.00 g/cm^3) x (66.0 cm^3) / (10.0 cm x 4.00 cm x 1.35 cm)

Density of block = 0.825 g/cm^3

A Rectangular Wooden Block Measures 10