In this experiment you will use a balancing method to determine the mass of a metre rule. You have been provided with: • a metre rule with a millimetre scale • a triangular block to act as a pivot • slotted masses making a total of 100 g. (a) Place the metre rule on the pivot. Place a mass m = 20g on the metre rule with its centre at the 5.0 cm mark. Adjust the position of the metre rule on the pivot until the metre rule is as close to balance as possible. The mass must stay at the 5.0 cm mark. [Figure 3.1] shows the balanced metre rule. [Figure 3.1]

1. (a)(i)Read the position of the pivot on the metre rule when the metre rule is balanced. The position of the pivot is the distance between the 0 cm mark on the rule and the tip of the pivot. Record the position of the pivot, in centimetres to the nearest millimetre, in Table 3.1 on page 10.[1]
2. (a)(ii)Calculate and record, in Table 3.1 on page 10: 1 the distance a between the 5.0 cm mark and the pivot 2 the distance b between the pivot and the 50.0 cm mark.[1]
3. (b)(i)Repeat the procedure in (a) for m = 40 g, 60 g, 80 g and 100 g.[2]
4. (b)(ii)Describe how you ensure that the centre of each mass placed on the metre rule is directly above the 5.0 cm mark.[1]
5. (c)Calculate the ratio r = b/a for each value of m. Record your answers in Table 3.1.[1]
6. (d)On the grid provided in Fig. 3.2 on page 11, plot a graph of r on the y-axis against m on the x-axis. Start your axes from the origin (0, 0). Draw the straight line of best fit.[4]
7. (e)(i)Calculate the gradient G of your graph. Show clearly on the graph how you obtained the numbers you use for your calculation, and show your working. G = .....................................................[2]
8. (e)(ii)The mass M of the metre rule is given by the equation shown. M = 1 / G Determine the mass of the metre rule to the nearest gram. M = .....................................................g[1]
9. (f)A student says that the centre of gravity of the metre rule is at the 50.0 cm mark. Describe how you use the apparatus provided to check that this statement is correct.[1]

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.