O-LevelPhysicsMeasurement5054/41 · May/June 2024 · Q110 Marks

A student finds the volume of a small glass ball (marble) by two different methods. (a) method 1 The student: • places six small glass balls by the side of a metre rule as shown in Fig. 1.1 • makes sure that there are no gaps between the balls. [Figure 1.1] metre rule

(a)(i)Take readings on the metre rule of the positions of points A and B shown in Fig. 1.1. Give your readings to the nearest 0.1 cm. position of point A = ................................................................ cm position of point B = ................................................................ cm[1]
(a)(ii)The length l on Fig. 1.1 is the distance between points A and B. The average diameter d of one ball can be found using the equation: l = 6d Use your answers to (a)(i) to calculate the length l and diameter d. Give your answers to the nearest 0.1 cm. l = ................................................................ cm d = ................................................................ cm[2]
(a)(iii)The average volume V of one glass ball using this method, is given by the equation: V = 3.14d³ / 6 Calculate V. V = .............................................................. cm³[1]
(b)(i)The student pours water into a measuring cylinder. • The volume of water in the measuring cylinder V₁ is shown in Fig. 1.2. [Figure 1.2] Write down the reading V₁. V₁ = .............................................................. cm³[1]
(b)(ii)• The six glass balls are carefully added to the water in the measuring cylinder. The new reading on the measuring cylinder V₂ is shown in Fig. 1.3. [Figure 1.3] The volume V_T of the six balls is given by V_T = V₂ - V₁. Calculate V_T. Show your working. V_T = .............................................................. cm³[1]
(b)(iii)Calculate the average volume V of one ball using this method. Give your answer to the nearest 0.1 cm³. V = .............................................................. cm³[1]
(c)Suggest whether method 1 or method 2 gives the more accurate value for the volume of the ball. Explain your answer. method giving more accurate value ........................................................................................ explanation ..............................................................................................................................[1]
(d)The student now uses the six glass balls to find the average mass of one glass ball using a small beaker and a top pan (electronic) balance. Describe the method the student uses.[2]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

[1] point A at 10.2 cm and B at 19.7 cm cao;
[1] l = 9.5 (cm) and d = 1.6 (cm);
[1] both to 0.1 cm;
[1] 2.1(4) (cm³);
[1] 27(.0) (cm³) cao ;
[1] (V2 value seen of 39 cm³ and) V₁ = 12(.0) cm³ ;
[1] average value of V correct from candidate's answer to (b)(ii) (2.0 cm³) ;
[1] method 1, as the measuring cylinder can only measure to the nearest 0.5 cm³ /1.0 cm³ or measuring the diameter to the nearest mm is more accurate. ;
[1] put beaker on balance and tare ;
[1] add 6 balls to find mass and divide by 6 ;
or
[1] put beaker on balance and record mass then add 6 balls to find mass again ;
[1] subtract the masses and divide answer by 6 ;