Density and upthrustEdexcel A-Level Physics: Subtopic test

1. 1
   A technician investigates a rectangular block of aluminium measuring 0.050 m × 0.040 m × 0.025 m. The block has a mass of 0.135 kg.

   (a)

   What is the volume of the block?

   [1 mark]

   • A5.0 × 10⁻² m³
   • B5.0 × 10⁻⁵ m³
   • C5.0 × 10⁻⁸ m³
   • D5.0 × 10⁻³ m³

   (b)

   What is the density of the aluminium?

   [1 mark]

   • A27 kg m⁻³
   • B270 kg m⁻³
   • C27 000 kg m⁻³
   • D2700 kg m⁻³

   (c)

   The block is cut into two equal halves. State what happens to the mass, volume and density of one half compared with the original block.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A wooden block of mass 0.48 kg and total volume 8.0 × 10⁻⁴ m³ is placed in fresh water of density 1000 kg m⁻³. It floats at rest. Take g = 9.81 N kg⁻¹.

   (a)

   What is the upthrust on the block?

   [1 mark]

   • A4.7 N
   • B7.8 N
   • C0.48 N
   • D4.8 × 10² N

   (b)

   What volume of the block is below the water surface?

   [1 mark]

   • A8.0 × 10⁻⁴ m³
   • B3.2 × 10⁻⁴ m³
   • C4.8 × 10⁻⁴ m³
   • D6.0 × 10⁻⁴ m³

   (c)

   Explain why the block floats with only part of its volume below the water surface.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A metal sphere is hung from a newtonmeter. In air the reading is 3.60 N. The sphere is then lowered until it is fully submerged in water of density 1000 kg m⁻³, without touching the container, and the reading falls to 2.25 N. Take g = 9.81 N kg⁻¹.

   (a)

   Calculate the volume of the sphere.

   [3 marks]

   (b)

   Determine the density of the metal and deduce whether a sphere made of the same metal would float in water.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A research submarine has an outside volume of 1500 m³, which does not change with depth. It operates in seawater of density 1030 kg m⁻³. Its ballast tanks can be flooded with seawater or emptied using compressed air. Take g = 9.81 N kg⁻¹.

   (a)

   Explain how the submarine can dive, hover at constant depth and return to the surface by changing the contents of its ballast tanks.

   [6 marks]

   (b)

   The submarine is hovering in seawater with its ballast correctly adjusted. It then drifts into estuary water of density 1005 kg m⁻³ without changing its ballast. Calculate the resultant force on the submarine and determine the mass of ballast water that must be removed to make it hover again.

   [6 marks]

   Total for question 4: 12 marks

End of questions