Fluids, density and pressure for Cambridge IGCSE Physics

Reading cue. The 5.0 cm and 3.0 cm are edges of the front face and the 2.0 cm runs into the page: three different edges, so no length is used twice, and 240 g is the mass of all of it.

1. aIdentify Identify which of the three edge lengths in Fig. 3.1 gives the depth of the block, and state how many faces of the block measure 5.0 cm by 3.0 cm.

   recall2 marks

   Check answer · 2 marks

   1. depth is the 2.0 cm edge, the one drawn receding into the page (1)
   2. two faces measure 5.0 cm by 3.0 cm, the front face and the hidden back face (1)

2. bCalculate A second block is cut from the same metal and measures 5.0 cm by 3.0 cm by 4.0 cm. Calculate its mass.

   routine3 marks

   Check answer · 3 marks

   1. volume of second block = 5.0 × 3.0 × 4.0 = 60 cm³ (1)
   2. volume of block in Fig. 3.1 = 30 cm³, so the second block has twice the volume, or 8.0 g in every cm³ used (1)
   3. mass = 480 g (1)

3. cExplain The block in Fig. 3.1 is cut in half by a single cut parallel to its 5.0 cm by 3.0 cm faces. State the volume and mass of one half, and explain what happens to the density of the metal.

   demanding4 marks

   Check answer · 4 marks

   1. volume of one half = 5.0 × 3.0 × 1.0 = 15 cm³ (1)
   2. mass of one half = 120 g (1)
   3. density is unchanged at 8.0 g/cm³ (1)
   4. mass and volume are both halved, so the mass in each cm³ is the same; density does not depend on how much material is present (1)

4. dSuggest The three edge lengths in Fig. 3.1 are all measured with the same ruler, so each carries the same uncertainty in centimetres. Suggest which of the three measurements limits the accuracy of any result calculated from them most severely, and justify your choice by comparison with the other two.

   top of the paper3 marks

   Check answer · 3 marks

   1. the 2.0 cm edge, the depth (1)
   2. taking the uncertainty as 0.1 cm for the sake of argument, that is 5% of 2.0 cm but about 3% of 3.0 cm and only 2% of 5.0 cm (1)
   3. the smallest length carries the largest percentage error, and because the three lengths are multiplied together that error passes into the volume (1)

Reading cue. The 50.0 cm³ is water alone and the 68.0 cm³ is water with the stone in, so the quantity everything turns on is the difference between the two levels, and it is printed on neither scale.

1. aDetermine Determine the volume of the stone from the two readings in Fig. 10.1.

   recall2 marks

   Check answer · 2 marks

   1. volume = 68.0 - 50.0 (1)
   2. = 18.0 cm³ (1)

2. bDetermine A second stone, identical to the first, is lowered into the same cylinder on a thread beside it. Determine the new reading of the water surface, and state one condition that must hold for your answer to be correct.

   routine3 marks

   Check answer · 3 marks

   1. the second stone displaces a further 18.0 cm³ (1)
   2. new reading = 68.0 + 18.0 = 86.0 cm³ (1)
   3. condition: both stones must be completely below the surface, and the water must not reach the top of the cylinder (1)

3. cExplain The cylinder in Fig. 10.1 is graduated in divisions of 1 cm³, so each of the two levels can be judged only to within half a division. Explain why the volume of the stone is known far less precisely than either reading, supporting your answer with figures.

   demanding3 marks

   Check answer · 3 marks

   1. each reading may be out by up to 0.5 cm³, so their difference may be out by up to 1 cm³ (1)
   2. 1 cm³ in 18.0 cm³ is about 6% (1)
   3. 0.5 cm³ in 68.0 cm³ is less than 1%, so subtracting two large readings to obtain a small difference magnifies the error (1)

4. dSuggest A larger stone is to be measured, but lowering it into the cylinder drawn in Fig. 10.1 would take the water above the top graduation. Suggest a change to the method that still uses the same cylinder, and explain why the volume obtained is still correct.

   top of the paper3 marks

   Check answer · 3 marks

   1. pour out some water first, so that the starting level is much lower, for example 20 cm³ rather than 50.0 cm³ (1)
   2. enough water must remain to cover the stone completely once it is lowered in (1)
   3. only the difference between the two readings is used, and that difference does not depend on the starting level (1)