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? The density of water is 1.00 g/cm³. 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 on the wooden block is equal to the weight of water displaced by the block. 
Volume of water displaced = (10.0 cm x 4.00 cm x 1.65 cm) = 66.0 cm^3 
Weight of water displaced = (66.0 cm^3) x (1.00 g/cm^3) x (9.81 m/s^2) = 647.5 g 
Buoyant force = weight of water displaced = 647.5 g 
The weight of the wooden block is calculated by finding the product of its volume and density: 
Weight of wooden block = (10.0 cm x 4.00 cm x 2.00 cm) x (density of wood) x (9.81 m/s^2) = 392.4 x (density of wood) g 
The block is in equilibrium, hence, the buoyant force must balance the weight of the block: 
Buoyant force = weight of block 
647.5 g = 392.4 x (density of wood) g 
Density of wood = 647.5 g / 392.4 cm^3 = 1.65 g/cm^3

Therefore, the answer is (A) 0.825 g/cm^3.

A Rectangular Wooden Block Measures 10