Turn over 9 5 A student measured the height h of a liquid column in a capillary tube. She used a travelling microscope to make measurements of the positions of the top and bottom of the liquid column. The travelling microscope consists of a simple microscope that can be moved vertically along a vernier scale. capillary tube h vernier scale eyepiece microscope liquid (a) The student used a capillary tube with an internal radius r equal to 0.10 mm and recorded the following readings from the vernier scale. Bottom of liquid column / cm Top of liquid column / cm 12.00 27.10 (i) State the uncertainty in each of these readings. (1) .................................................................................................................................................................................................................................................. (ii) Calculate the percentage uncertainty in the student’s value of h. (2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. Percentage uncertainty in h = ....................................................... 10 (iii) The student repeated the measurement of h for capillary tubes of different radii. The table shows the student’s final data. r / mm 1/r h / cm 0.09 11.1 16.56 0.10 10.0 15.1 0.12 8.3 12.6 0.15 6.7 10.33 Criticise the student’s recording of the data. (2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (b) The student plotted the following graph. 12.0 11.0 10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 1 r / mm−1 20.0 15.0 10.0 5.0 0.0 h / cm Turn over 11 (i) Determine the height of the liquid column that the student could expect for a tube with an internal radius of 0.11 mm. (3) ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... Height of liquid column = ....................................................... (ii) In her notes it stated that h = k r where k is constant Assess the extent to which the student’s data supports this relationship. (4) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (Total for Question 5 = 12 marks)