Density: Physics 0625 (Cambridge O Level / IGCSE)

A small ornament made from a single material has a mass of $63\text{ g}$ and a volume of $18\text{ cm}^3$. What is the density of the material?

A student is investigating a rectangular metal block for a science project.

(a) The block measures $4.0\text{ cm}$ by $5.0\text{ cm}$ by $2.0\text{ cm}$. Calculate the volume of the block. [1]

(b) The block has a mass of $168\text{ g}$. Calculate the density of the metal, giving your answer in $\text{g/cm}^3$. [2]

(c) The density of aluminium is $2.7\text{ g/cm}^3$. State, with a reason, whether the block could be made of aluminium. [1]

A student wants to find the density of an irregularly shaped stone using the displacement method.

(a) Describe how the student could use a measuring cylinder and a balance to determine the volume and mass of the stone. [2]

(b) The measuring cylinder contains $42.0\text{ cm}^3$ of water. When the stone is fully lowered into the water, the level rises to $57.5\text{ cm}^3$. The mass of the stone is $38.7\text{ g}$. Calculate the density of the stone, giving your answer to 3 significant figures. [3]

(c) State one precaution the student should take to obtain an accurate value for the volume of the stone. [1]

Liquid P and liquid Q do not mix. Liquid P has a density of $0.80\text{ g/cm}^3$ and floats on top of liquid Q, which has a density of $1.26\text{ g/cm}^3$, inside a tall glass cylinder. A small solid sphere of density $1.05\text{ g/cm}^3$ is dropped gently into the cylinder from above.

(a) State where the sphere finally comes to rest, and explain your answer by comparing densities. [2]

(b) The sphere has a volume of $12.0\text{ cm}^3$. Calculate the mass of the sphere. [2]

(c) Convert the density of liquid Q, $1.26\text{ g/cm}^3$, into $\text{kg/m}^3$. [2]

A metalworker makes an alloy by melting and thoroughly mixing $50.0\text{ cm}^3$ of metal A, which has a density of $8.90\text{ g/cm}^3$, with $30.0\text{ cm}^3$ of metal B, which has a density of $7.14\text{ g/cm}^3$. Assume the total volume of the alloy formed equals the sum of the two original volumes.

(a) Calculate the mass of metal A and the mass of metal B used. [2]

(b) Calculate the density of the alloy formed. [3]

(c) The alloy is placed in water, which has a density of $1.00\text{ g/cm}^3$. State, with a reason, whether the alloy floats or sinks. [1]

A bottle contains a sample of vegetable oil. The oil has a density of $0.92\text{ g/cm}^3$ and a mass of $138\text{ g}$. What is the volume of the oil?

A student wants to determine the density of an unknown liquid, liquid X, using a measuring cylinder and a digital balance.

(a) Describe how the student could use the measuring cylinder and the balance to find the mass and the volume of the liquid. [2]

(b) The empty measuring cylinder has a mass of $32.0\text{ g}$. After liquid X is poured in, the total mass is $109.0\text{ g}$, and the volume reading on the cylinder is $50.0\text{ cm}^3$. Calculate the density of liquid X. [2]

(c) A sample of liquid X is poured gently into a beaker of water (density $1.00\text{ g/cm}^3$), and the two liquids do not mix. State, with a reason, whether liquid X floats on top of the water or sinks below it. [1]

A workshop technician turns a solid metal cylinder on a lathe. The cylinder has a diameter of $4.0\text{ cm}$ and a height of $6.0\text{ cm}$.

(a) Calculate the volume of the cylinder, using $V = \pi r^2 h$. Give your answer to 3 significant figures. [2]

(b) The cylinder has a mass of $670\text{ g}$. Calculate the density of the metal. [2]

(c) A second, identical cylinder of the same metal is welded end-to-end onto the first, forming one long cylinder of twice the length. State the density of this combined cylinder, giving a reason. [1]

A student measures the mass of several different volumes of a liquid to investigate how mass and volume are related. The results are shown in the table below.

A graph of mass against volume for these results is a straight line through the origin.

(a) Use the two most widely separated data points to calculate the gradient of the graph, and state what physical quantity this gradient represents. [2]

(b) Explain, in terms of mass and volume, why the graph is a straight line that passes through the origin. [2]

(c) Use your answer to part (a) to predict the mass of $150\text{ cm}^3$ of the liquid. [2]

A hollow plastic buoy used to mark a shipping channel is made from a shell of solid plastic, of density $1.40\text{ g/cm}^3$, moulded around a sealed, empty air space. The mass of the plastic shell is $850\text{ g}$, and the total external volume of the buoy (the plastic shell plus the air space it encloses) is $2400\text{ cm}^3$. The mass of the air inside the buoy is negligible.

(a) Calculate the average (overall) density of the buoy, using its total mass and its total external volume. Give your answer to 3 significant figures. [2]

(b) The buoy floats in seawater of density $1.03\text{ g/cm}^3$. State, with a reason based on your answer to part (a), whether this is consistent with the buoy floating. [2]

(c) The plastic itself has a density of $1.40\text{ g/cm}^3$, which is greater than the density of seawater. Explain why the buoy is still able to float. [2]