Density

The mass and volume of four distinct objects are plotted in the diagram shown. Which object has the lowest density?

May/June 2015

Fig. 2.1 depicts two engineers checking the length of a wall built from concrete. The wall has a height of $2.0\,\text{m}$, a length of $15\,\text{m}$ and a thickness of $0.25\,\text{m}$. Its weight is $180\,000\,\text{N}$ and its mass is $18\,000\,\text{kg}$.

May/June 2015

Fig. 3.1 presents a very thin plastic sheet. A student attempts to find the sheet's thickness with a ruler, but the sheet is too thin for an accurate reading. The student measures the mass of the sheet and records $0.12\,\text{g}$.

May/June 2016

A student carries out an investigation into the density of several liquids. Fig. 3.1 gives a table of her results.

May/June 2016

A diagram presents a rectangular block whose dimensions are $5.0\,\text{cm}$, $4.0\,\text{cm}$ and $3.0\,\text{cm}$. Its density is $2.5\,\text{g cm}^{-3}$. Calculate the mass of the block.

May/June 2017

Fig. 3.1 shows a jar containing 50 small glass beads that vary in size and shape.

May/June 2018

A student is working out the density of copper by using a balancing method. The apparatus is arranged as shown in Fig. 4.1.

May/June 2018

A student measures the mass and volume of two irregular-shaped objects, one iron and the other copper, using the apparatus shown in Fig. 1.1. Table 1.1 gives the outcomes obtained.

May/June 2019

A measuring cylinder initially contains $100\,\text{cm}^3$ of liquid paraffin, and water is then poured in. (The density of paraffin is $0.80\,\text{g cm}^{-3}$, while the density of water is $1.0\,\text{g cm}^{-3}$.) When the water has been added, the paraffin level increases to $150\,\text{cm}^3$. The paraffin and water do not mix. What is the final total mass of liquid in the measuring cylinder?

May/June 2021

Air is enclosed in a cylinder by means of a piston. The piston is pushed inwards, causing the air volume to decrease. At the starting volume, the density of the air in the syringe is $0.0012\ \text{g cm}^{-3}$. What is the density of the air in the syringe at the final volume?

May/June 2021

A plastic cube, with density $\rho$, is compressed until every edge is reduced to one-half of its initial length. What is the density of the cube’s material after compression?

May/June 2022

A measuring cylinder that contains water is placed on a balance. A stone is then lowered into the water. The diagram shows the readings on the balance and the measuring cylinder. What is the stone’s density?

May/June 2022

A student measures the density of a solid metal cube. Which items of equipment does the student need?

May/June 2023

A student measures the density of a liquid. Which apparatus does the student use?

May/June 2023

Cubes $X$ and $Y$ each have the same mass, and the side length of $X$ is twice the side length of $Y$. What is the value of the ratio $\dfrac{\text{density of } X}{\text{density of } Y}$?

May/June 2024

A group of students measures the masses and volumes of wood samples of different sizes. Which graph represents their results?

May/June 2025

A student measures the density of a small rock. The weight of the small rock is $1.2\,\text{N}$. She adds $100\,\text{cm}^3$ of water to a measuring cylinder. She then lowers the rock carefully into the $100\,\text{cm}^3$ of water. The measuring cylinder now reads $147\,\text{cm}^3$. What is the density of the rock?

May/June 2025

When a metal ball drops through a liquid, the liquid provides a frictional force on the ball that acts against the ball’s motion. Design an experiment to find out how the density of a liquid in a measuring cylinder is related to the average speed of a metal ball as it falls through the liquid from the surface to the base of the cylinder. The average speed of the ball is found from: average speed $= \dfrac{\text{distance travelled}}{\text{time taken}}$. The setup of the apparatus is shown in Fig. 4.1.

May/June 2025

In an experiment to determine the density of a stone, the stone is placed into a measuring cylinder that is partially filled with water. Which statement is correct?

Oct/Nov 2015

Cylinders P and Q are both made from copper. The height of P is 2 times the height of Q. The diameter of P is 1/2 the diameter of Q. Which statement is correct?

Oct/Nov 2015

In an experiment to determine the density of a stone, the stone is placed into a measuring cylinder that already contains some water. Which statement is correct?

Oct/Nov 2015

Gold has a density of $19\,\text{g cm}^{-3}$. A gold coin has a thickness of $2.0\,\text{mm}$. The area of each face of the coin is $4.5\,\text{cm}^2$. What is the coin's mass?

Oct/Nov 2016

A student wants to find the density of a liquid. She transfers the liquid into a measuring cylinder, as shown in Fig. 1.1.

Oct/Nov 2016

Two blocks are connected together. One block has a density of $6.0\,\text{g cm}^{-3}$, while the other has a density of $9.0\,\text{g cm}^{-3}$. What is the combined density of the two blocks when they are joined together?

Oct/Nov 2017

Two cylinders P and Q are made from copper. The height of P is double the height of Q. The diameter of P is half that of Q. Which statement is correct?

Oct/Nov 2018

Cylinders P and Q are both constructed from copper. The height of P is twice that of Q, and the diameter of P is half that of Q. Which statement is correct?

Oct/Nov 2018

A student is handed a beaker containing some liquid and is asked to work out the liquid’s density. Density is calculated with the equation $\text{density} = \frac{\text{mass}}{\text{volume}}$. He transfers the liquid into a measuring cylinder. Fig. 3.1 shows the measuring cylinder after the liquid has been poured in.

Oct/Nov 2018

An electronic balance is set up to indicate the weight of any object placed on its upper plate. Fig. 5.1 shows the balance with an empty measuring cylinder on the upper plate. Fig. 5.2 illustrates how the balance reading changes as the volume of oil in the measuring cylinder increases.

Oct/Nov 2019

A student carries out an experiment to determine the density of water.

Oct/Nov 2019

What expression is used to determine density?

Oct/Nov 2020

A stone is put into a measuring cylinder containing water, as illustrated. Before the stone is added, the water volume in the cylinder is $15\,\text{cm}^3$ and the stone’s mass is $90\,\text{g}$. What is the stone’s density?

Oct/Nov 2021

A student makes measurements in order to determine the density of a regularly shaped block. Which formula is used to work out the block’s density?

Oct/Nov 2021

A student determines the density of an object with an irregular shape. He selects his apparatus from this list: 1 stop-watch 2 measuring cylinder 3 balance Which apparatus does the student have to use?

Oct/Nov 2022

The supports beneath a building are long concrete cylinders with a pointed end. A pile-driver is a machine used to drive these pointed concrete cylinders into the ground. Fig. 2.1 shows a pile-driver. A heavy block with a mass of $2.9 \times 10^4\,\text{kg}$ is raised into the air and then released onto the top of a concrete cylinder. This makes the cylinder sink into the ground. Fig. 2.2 shows the heavy block. The block has a height of 2.0 m and a cross-sectional area of $1.8\,\text{m}^2$.

Oct/Nov 2022

A student determines the density of a sample of modelling clay. The clay is shaped into a cube, as illustrated in Fig. 3.1.

Oct/Nov 2022

A student determines that a rock has a mass of $65\,\text{g}$. She pours $30\,\text{cm}^3$ of water into a measuring cylinder. She then lowers the rock into the water until it is fully covered. The water level increases to $55\,\text{cm}^3$. What is the density of the rock?

Oct/Nov 2023

The density of a material is $2.4\,\text{g cm}^{-3}$. What is this density in $\text{kg m}^{-3}$?

Oct/Nov 2024

A student works out an approximate density for the glass used to make a test-tube. In Fig. 1.1, a full-size drawing of the test-tube shows the height $h$ and the external diameter $d$.

Oct/Nov 2024

The diagram shows a solid metal block. Which equation is used to calculate the density of the metal that the block is made from?

Oct/Nov 2025

A student determines the density of an irregularly shaped stone. Which pieces of equipment are required?

Oct/Nov 2025