2.3 Measuring Density
23.1 – Measuring densities of various objects
We can find out the density of liquid, regular and irregular shaped solids.
Density of regular shaped solid objects
- Measure the object’s dimensions like width, height, length, or radius using a ruler. Then, calculate its volume using the appropriate formula.
- If it is sphere, volume is calculated by using V=\( \frac{4}{ 3}\) πr3.
- If it is cylinder, volume is calculated by using V= πr2×d.
- Where r represents the radius and d is the length or height.
- If it is cube, volume is calculated by using V= d3.
- Measure the mass of the object by placing it on a digital balance.
- Repeat the experiment many times and take average of the results.
- By using p=\( \frac{m}{ v}\)
, determine the density of object.
Irregular shape Density by Displacement Method
Example: Two liquids 1 and 2 having density 0.5\( \frac{kg}{ m^3}\) and 0.76\( \frac{kg}{ m^3}\) respectively. If both of these liquids are not mixed, then which liquid will float on the top of other?
Solution:
Density of liquid 1 = 0.5\( \frac{kg}{ m^3}\)
Density of liquid 2 = 0.76\( \frac{kg}{ m^3}\)
Only the liquid whose density is lower, floats on the other. As the density of liquid 1 is lesser than liquid 2, so liquid 1 will float over liquid 2.
Example: A block of wood has a volume of 210cm3 and mass is 180g.
- Calculate the density of block of wood.
- The block is held just above the surface of liquid of density 0.88\( \frac{g}{ m^3}\). Predict and explain what happens when block is released.
Solution:
As we know that
Density = \( \frac{Mass}{ volume}\)= \( \frac{180}{ 120}\)= 0.86\( \frac{kg}{ m^3}\)
Its given that density of liquid is 0.88\( \frac{g}{ m^3}\). The density of block is smaller than the density of liquid. Therefore, the block will float.
While checking the level of oil in the tank, the man drops a brass key into the oil and it sinks into the bottom of the oil.
- State what this shows about the density of brass.
- Explain how attaching the key to the piece of wood could prevent the key from sinking.
Solution:
- An object floats if its density is less than that of the liquid and sinks if its density is greater. Since the brass key sinks in oil, the key’s density is higher than that of the oil.
- If the combined density of wood and brass key is less than the density of oil, the combination will float, preventing the brass key from sinking.
Definitions
Density: It is mass per unit volume of an object.
Floating: The object will float only if the object’s upthrust is equal to or greater than its weight.
Sinking: The object will sink if the upthrust is less than its weight.
- Measure the mass of the irregular object.
- Use a measuring cylinder to find the initial and final water volumes when the object is submerged.
- Note the reading on the measuring cylinder which will be the volume of displaced water.
- The volume of the object is the difference between these water volumes.
- Repeat the experiment many times for accuracy and take the average of the results.
Once the volume and mass are known, you can determine the density of the object by using the formula: ρ =\( \frac{m}{V}\)
❓ Exam Question
0625/0972/21-Oct-Nov-2020-Q6
A metal ball is attached to a cork and is lowered into a measuring cylinder, pulling the cork into the water, as shown.
The mass of the cork is 4.8 g.
What is the density of the cork?
Density of liquid
To measure the density of a liquid
- Measure the mass of the measuring cylinder by placing it on a digital balance.
- Fill the cylinder halfway with the liquid and record its volume. Also, record the new reading on the digital balance.
- Repeat the experiment and take the average value of the results.
- Determine the mass of the liquid by subtracting the final reading from the initial reading of the measuring cylinder: Mass of liquid=Mass of cylinder with liquid−Mass of empty cylinderMass of liquid=Mass of cylinder with liquid−Mass of empty cylinder.
- Once the mass and volume of the liquid are known, calculate the density using the formula: ρ =\( \frac{m}{V}\)
Example: Two liquids 1 and 2 having density 0.5\( \frac{kg}{ m^3}\) and 0.76\( \frac{kg}{ m^3}\) respectively. If both of these liquids are not mixed, then which liquid will float on the top of other?
Solution:
Density of liquid 1 = 0.5\( \frac{kg}{ m^3}\)
Density of liquid 2 = 0.76\( \frac{kg}{ m^3}\)
Only the liquid whose density is lower, floats on the other. As the density of liquid 1 is lesser than liquid 2, so liquid 1 will float over liquid 2.
Example: A block of wood has a volume of 210cm3 and mass is 180g.
- Calculate the density of block of wood.
- The block is held just above the surface of liquid of density 0.88\( \frac{g}{ m^3}\). Predict and explain what happens when block is released.
Solution:
As we know that
Density = \( \frac{Mass}{ volume}\)= \( \frac{180}{ 120}\)= 0.86\( \frac{kg}{ m^3}\)
Its given that density of liquid is 0.88\( \frac{g}{ m^3}\). The density of block is smaller than the density of liquid. Therefore, the block will float.
While checking the level of oil in the tank, the man drops a brass key into the oil and it sinks into the bottom of the oil.
- State what this shows about the density of brass.
- Explain how attaching the key to the piece of wood could prevent the key from sinking.
Solution:
- An object floats if its density is less than that of the liquid and sinks if its density is greater. Since the brass key sinks in oil, the key’s density is higher than that of the oil.
- If the combined density of wood and brass key is less than the density of oil, the combination will float, preventing the brass key from sinking.
Definitions
Density: It is mass per unit volume of an object.
Floating: The object will float only if the object’s upthrust is equal to or greater than its weight.
Sinking: The object will sink if the upthrust is less than its weight.