1. 1
   A jeweller wants to check whether a metal ring is made of pure gold by measuring its mass and volume separately and comparing the result to the known density of gold.

   (a)

   Which equation should the jeweller use to calculate the density of the ring?

   [1 mark]

   • Adensity = mass ÷ volume
   • Bdensity = mass × volume
   • Cdensity = volume ÷ mass
   • Ddensity = mass × gravitational field strength

   (b)

   Which unit is correct for density?

   [1 mark]

   • AN/m³
   • Bkg/m³
   • Ckg·m³
   • DN/m²

   (c)

   The ring has a mass of 38.6 g and a volume of 2.0 cm³. Calculate the density of the ring in g/cm³ and state whether this is consistent with pure gold, which has a density of 19.3 g/cm³.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A student stands on ice wearing narrow-heeled boots and notices she sinks into the snow much more than her friend, who is wearing snowshoes with a much larger surface area, even though the two students weigh the same.

   (a)

   Which equation explains why the snowshoes reduce sinking?

   [1 mark]

   • Apressure = force × time
   • Bpressure = force × area
   • Cpressure = mass ÷ volume
   • Dpressure = force ÷ area

   (b)

   Compared with the narrow-heeled boots, what effect do the snowshoes have on the pressure exerted on the snow for the same body weight?

   [1 mark]

   • AThe pressure is increased
   • BThe pressure stays exactly the same
   • CThe pressure is decreased
   • DThe pressure becomes zero

   (c)

   The student weighs 600 N. Her narrow-heeled boots have a total contact area of 0.002 m² and the snowshoes have a total contact area of 0.5 m². Calculate the pressure she exerts on the snow while wearing each type of footwear.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A deep-sea submersible is designed to explore the ocean floor at great depth.

   (a)

   Explain why the pressure exerted by the seawater on the hull of the submersible increases as it descends, and why the pressure acts equally on all surfaces of the hull rather than only pushing downwards.

   [3 marks]

   (b)

   The submersible descends to a depth of 2000 m in seawater of density 1030 kg/m³, with a gravitational field strength of 10 N/kg. Calculate the pressure due to the water alone at this depth, and explain one design feature the engineers must consider as a result of this value.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A historic canal system uses a simple lock filled with water to raise and lower boats between different water levels. Engineers need to design the lock gates to withstand the pressure of the water.

   (a)

   Explain, using the relevant physics of pressure in liquids, how the pressure exerted by the water on the lock gates varies with depth and how this affects the way the gates must be constructed.

   [6 marks]

   (b)

   The canal lock is filled with fresh water of density 1000 kg/m³ to a depth of 5 m against the gates, with a gravitational field strength of 10 N/kg. Each gate has a submerged area of 15 m² in contact with the water. Calculate the average pressure and the total force acting on one gate, and discuss why engineers might use the average pressure over the whole gate rather than the maximum pressure at the bottom when designing the gate's overall strength.

   [6 marks]

   Total for question 4: 12 marks

End of questions