A student does an experiment to find the mass of a metre rule. (a) A fixed mass is placed on the metre rule at the 5.0 cm mark as shown in Fig. 3.1. [Figure 3.1] The student: • places the pivot below the 25.0 cm mark on the metre rule • places a mass of mass m = 20g on the metre rule • adjusts the position of the 20g mass until the rule is as close to balance as possible.

1. (a)(i)The position of the 20g mass when the rule is as close to balance as possible is shown in Fig. 3.2. [Figure 3.2] Using Fig. 3.2, determine the distance d of the centre of the 20g mass from the pivot when the metre rule is as close to balance as possible. d = .................................................... cm[1]
2. (a)(ii)Describe the technique the student uses to balance the metre rule with the 20g mass.[1]
3. (a)(iii)• The student repeats the procedure for values of mass m = 30g, 40g, 50 g and 60 g. Table 3.1 shows the results. Add your value of d for mass m = 20 g in (a)(i) to Table 3.1. Calculate 1/d for each mass m, and record all values in Table 3.1. Give your answers to an appropriate number of significant figures. [Table 3.1][2]
4. (a)(iv)Suggest why a value of d cannot be found for mass m = 10g.[1]
5. (b)(i)Using the grid provided in Fig. 3.3 on page 13, plot a graph of 1/d 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]
6. (b)(ii)Calculate the gradient G of your line. Show all your working, and indicate on the graph the values you use. G = ....................................................[2]
7. (c)The mass M of the metre rule can be calculated using the equation: M = 160 - 0.040 / G Use your value of G in (b)(ii) to calculate M. M = .................................................... g[1]
8. (d)The student is given a piece of modelling clay. He places it on the metre rule as shown in Fig. 3.4. He finds that the metre rule is balanced when the modelling clay is a distance of 40.0 cm from the pivot. [Figure 3.4] Using your graph in Fig. 3.3 on page 13, find the mass of the piece of modelling clay. Show your working. mass of piece of modelling clay = .................................................... g[2]

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