Density, upthrust and viscous dragEdexcel International A Level Physics: Subtopic test

1. 1
   A student has a solid metal cube of side 2.0 cm. Its mass, measured on a balance, is 21.6 g.

   (a)

   What is the volume of the cube in m³?

   [1 mark]

   • A8.0 × 10⁻³ m³
   • B8.0 × 10⁻⁶ m³
   • C4.0 × 10⁻⁴ m³
   • D6.0 × 10⁻² m³

   (b)

   What is the density of the metal?

   [1 mark]

   • A2.7 × 10³ kg m⁻³
   • B2.7 kg m⁻³
   • C2.7 × 10⁶ kg m⁻³
   • D3.7 × 10⁻⁴ kg m⁻³

   (c)

   The student has another solid object with an irregular shape that fits inside a measuring cylinder of water. Describe how the student could determine its density.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A solid cube of side 0.10 m and mass 0.80 kg is held fully submerged in water of density 1000 kg m⁻³. The acceleration of free fall is 9.81 m s⁻².

   (a)

   What is the volume of water displaced by the cube?

   [1 mark]

   • A8.0 × 10⁻⁴ m³
   • B1.0 × 10⁻² m³
   • C1.0 × 10⁻³ m³
   • D1.0 × 10⁻¹ m³

   (b)

   What is the upthrust on the cube?

   [1 mark]

   • A7.8 N
   • B1.0 N
   • C0.98 N
   • D9.8 N

   (c)

   The cube is released from rest. Calculate the resultant force on it at the instant of release, and state its direction.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A steel ball bearing of radius 2.0 mm and density 7800 kg m⁻³ is released from rest at the surface of a tall tank of glycerol. The glycerol has density 1260 kg m⁻³ and viscosity 0.95 Pa s at the temperature of the experiment. The ball falls through the glycerol and reaches a constant terminal velocity. The acceleration of free fall is 9.81 m s⁻².

   (a)

   Calculate the weight of the ball and the upthrust on it when it is fully submerged.

   [3 marks]

   (b)

   Calculate the terminal velocity of the ball in the glycerol.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Students use the falling-ball method to determine the viscosity of a transparent oil, which has a density of 900 kg m⁻³. They use small steel ball bearings of density 7800 kg m⁻³ and a tall transparent measuring cylinder filled with the oil. The acceleration of free fall is 9.81 m s⁻².

   (a)

   Describe how the students could use this method to determine the viscosity of the oil. Include the measurements they should take and how the viscosity is calculated.

   [6 marks]

   (b)

   A student uses a ball of radius 1.5 mm. It falls 0.30 m between two marks in 2.5 s at a constant speed. Determine the viscosity of the oil and evaluate how reliable this value is, referring to the conditions for the use of Stokes' law and to temperature.

   [6 marks]

   Total for question 4: 12 marks

End of questions