Density and floating in equilibrium – problems and solutions

1. A block placed into two liquids with different types. In liquids A, 0.6 part of an object is in the liquid. In liquids B, 0.5 part of an object is in the liquid. Determine the ratio of the density of liquid A to liquid B.

Known :

Density of block = x

Part of the object in liquid A = 0.6

The density of liquid A = y

Part of object in liquid B = 0.5

The density of liquid B = z

Wanted: The ratio of the density of liquid A to liquid B (y: z)

Solution :

Substitute x in equation 2 with x in equation 1 :

2. An object placed in liquid P, 0.5 part of the object is in liquid. When the object placed in liquid Q, the object is in liquid, as shown in the figure below. What is the ratio of the density of liquid P to liquid Q?

Known :

Density of object = x

Part of object in liquid P = 1/2 = 0.5

The density of liquid P = y

Part of the object in liquid Q = 1

The density of liquid Q = z

Wanted: The ratio of the density of liquid P to liquid Q (y: z)

Solution :

Substitute x in equation 2 with x in equation 1 :

3. A wood floating in oil (density of oil is 800 kg/m³). 4/5 parts of the wood are in the oil. What is the density of the wood?

Known :

Density of oil (ρ) = 800 kg/m^-3

Part of wood in oil = 4/5

Wanted: Density of wood

Solution :

The density of wood is 640 kg/m³.

4. The weight of a block is 50 N. In water, the weight of the block is 30 N. If the density of water is 10³ kg/m^-3 what is the density of block.

Known :

Weight of block in air (w) = 50 N

Weight of block in water (w_water) = 30 N

Density of water (ρ_water) = 10³ kg/m³ = 1000 kg/m³

Acceleration due to gravity (g) = 10 m/s²

Mass of block (m) = w/g = 50/10 = 5 kg

Wanted : Density of block (ρ_block)

Solution :

Buoyant force :

F_A = w – w_water = 50 – 30 = 20 N

Volume of block in water :

F_A = ρ g V

20 = (1000)(10) V

20 = (10,000) V

V = 20/10,000

V = 0.002 m³

Density of block :

ρ = m/V = 5 / 0.002 = 2500 kg/m³

5. A wood block dipped in water. 25% of its part is above the surface of water and 75% is in water. Density of water is 1 g/cm³ and acceleration due to gravity is 10 m/s². Determine the density of the blocks.

A. 0.025 kg/m³

B. 0.075 g/cm³

C. 0.250 kg/m³

D. 0.750 g/cm³

Known :

Part of block above the surface of water = 25% = 25/100 = 0.25

The part of block in water = 75% = 75/100 = 0.75

The density of water (ρ_water) = 1 g/cm³ = 1000 kg/m³

Acceleration due to gravity = 10 m/s²

Wanted : Density of block (ρ_block)

Solution :

Volume of block in water = the ratio of the density of block to the density of water

The correct answer is D.