Density is the ratio of the mass of a substance to the volume of that substance. It is a scalar quantity.
When two substances, say A and B are mixed, the density of the mixture AB can be calculated by dividing the mass of the mixture by the volume of that mixture.
It can also be broken down to
When we say relative density, we are trying to compare the density of a substance to that of water. Relative density is the ratio of the mass of a liquid to the mass of an equal volume of water. Relative density has no unit. It is also called specific gravity. There are different method of calculating the relative density of liquid. We shall be looking at them one after the other.
Relative Density can also be calculated using a density bottle. Let's say I want to get the relative density of kerosene, first thing to do is to get the weight of the bottle and record it, after which I will fill the bottle with water and get the weight and record, empty the bottle and fill it with the liquid (Kerosene) and also get the weight, then use the data gotten and apply this formula
When the data is gotten in kilogram, this can be use
Where M1 and W1 represent the mass and weight of the empty bottle.
Where M2 and W2 represent mass and weight of bottle with liquid.
Where M3 and W3 represent mass and weight of bottle with water.
Relative density of a liquid can also be calculated using this formula
Upthrust is the apparent weight loss of an object.
W - W1 is the difference between the weight of an object in air and the weight of an object in liquid.
W – W2 is the difference between the weight of an object in air and the weight of an object in water.
Where M and W represent the mass and weight of the body in air.
Where M1 and W1 represent the mass and weight of the body in liquid.
Where M2 and W2 represent the mass and weight of the body in water.
Relative Density of a liquid can also be calculated by dividing the density of the liquid to the density of water.
Relative density of a liquid can also be calculated using Hare’s apparatus
Pressure generated at water = pressure generated at liquid
Relative density of solid is the ratio of the weight of the solid to upthrust experienced in water. It can be calculated using this formula
Where ‘W’ represent the weight of the solid in air and W1 represent the weight of the solid in water.
This principle states that if a body is wholly or partially immersed in a fluid, it will experience an upthrust which is equal to the weight of the fluid displaced.
Upthrust = weight of fluid displaced
Upthrust = mass of fluid displaced * g
Upthrust = density * volume * g
This law states that a body will float only when the upthrust is equal to the weight of the body.
Question: What makes a ship to float in water?
Answer: It is because a ship has a hollow space in it, as a result, the average weight of the ship is lower than the liquid displaced.
Question: what makes a pin thrown into water sink?
Answer: it is because the upthrust is too small compare to the weight of the ship.
Examples
- A 3m³ volume of liquid W of density 200kg/m³ is mixed with another liquid A of volume 7m³ and density 150kg/m³. The density of the mixture is
- A copper cube weighs 0.25N in air, 0.17N when completely immersed in paraffin oil and 0.15N when completely immersed in water. The ratio of upthrust in oil to upthrust in water is ?
Solution
Weight in air,(W) =0.25N, weight in paraffin oil(W1) = 0.17N, weight in water(W2) =0.15N
- A balloon whose volume is 300m³ is filled with hydrogen. If the density of air is 1.3kg/m³. Find the upthrust on the balloon(g=10m/s²)
- The density of certain oil on frying becomes 0.4kg/m³ with a volume of 20m³. What will be its initial volume when its initial density is 0.8kg/m³ assuming no loss of oil due to spillage?
- An empty relative density bottle has a mass of 30kg. when filled with paraffin oil, its mass is 70kg, calculate the mass of the bottle when it is filled with water(relative density of paraffin = 0.8)
- Two liquids L1 and L2 are contained in a U-tube. The height and the density of L1 are 8cm and 1000kg/m³ respectively. If the density of L2 is 800kg/m³ its height measured from the same level is
- In the Hare’s apparatus, water rises to a height of 26.5cm in one limb. If a liquid rises to a height of 20.4cm in the other limb, what is the relative density of the liquid
- An object weighs 22kg in water and 30kg in air. What is the upthrust exerted by the liquid on the object?(g=10m/s²)
Solve the exercises and write your answers in the comment section below.