A student uses a balancing method to determine the mass of a metre rule.

1. (a)(i)The student: • places the metre rule on a pivot • places a mass m = 20g on the metre rule with its centre at the 5.0 cm mark • adjusts the position of the metre rule on the pivot until the metre rule is as close to balance as possible. Fig. 3.1 shows the balanced metre rule. Fig. 3.2 shows the position of the pivot under the metre rule when the metre rule is balanced. Read the position of the pivot on the metre rule when the metre rule is balanced. Record the reading 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 5.0cm mark and the pivot 2 the distance b between the pivot and the 50.0 cm mark.[1]
3. (b)The student repeats the procedure in (a) for m = 40g, 60g, 80 g and 100 g. The results are shown in Table 3.1. Describe how the student makes sure that the centre of each mass placed on the metre rule is directly above the 5.0cm mark.[1]
4. (c)Calculate the ratio r = b/a for m = 20 g. Record, in Table 3.1, your answer to two significant figures.[2]
5. (d)On the grid provided in Fig. 3.3 on page 11, plot a graph of r on the y-axis against m on the x-axis. Start from the origin (0, 0). Draw the straight line of best fit.[4]
6. (e)(i)Calculate the gradient G of your graph. Show clearly on the graph how you obtained the numbers you use for your calculation.[2]
7. (e)(ii)The mass M of the metre rule in grams is given by the equation: M = 1/G Determine the mass of the metre rule to the nearest gram.[1]
8. (e)(iii)Name a piece of apparatus that the student can use to measure the mass of the metre rule directly.[1]
9. (f)A student says that the centre of mass 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]

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