Page 32 15. A student constructs a simple air-insulated capacitor using two parallel metal plates, each of area A, separated by a distance d. The plates are separated using small insulating spacers as shown in Figure 15A. metal plates capacitance meter d air gap insulating spacer Figure 15A The capacitance C of the capacitor is given by 0 A C ε d = The student investigates how the capacitance depends on the separation of the plates. The student uses a capacitance meter to measure the capacitance for different plate separations. The plate separation is measured using a ruler. The results are used to plot the graph shown in Figure 15B. The area of each metal plate is 9·0 × 10−2 m2. 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 0.00 0.20 0.40 0.60 Figure 15B y = 8·3x − 0.20 C (× 10−10 F) (× 103 m−1 ) 0.80 1.00 1.20 1 d Page 33 MARKS DO NOT WRITE IN THIS MARGIN 15. (continued) (a) (i) Use information from the graph to determine a value for εo, the permittivity of free space. Space for working and answer (ii) Use your calculated value for the permittivity of free space to determine a value for the speed of light in air. Space for working and answer (b) The best fit line on the graph does not pass through the origin as theory predicts. Suggest a reason for this. [Turn over 3 3 1 Page 34 [BLANK PAGE] do not write on this page Page 35 MARKS DO NOT WRITE IN THIS MARGIN 16. A student uses two methods to determine the moment of inertia of a solid sphere about an axis through its centre. (a) In the first method the student measures the mass of the sphere to be 3·8 kg and the radius to be 0·053 m. Calculate the moment of inertia of the sphere. Space for working and answer (b) In the second method, the student uses conservation of energy to determine the moment of inertia of the sphere. The following equation describes the conservation of energy as the sphere rolls down the slope 2 2 1 1 2 2 mgh mv Iω = + where the symbols have their usual meanings. The equation can be rearranged to give the following expression 2 2 2 1 I gh v mr ⎛ ⎞ = + ⎜ ⎟ ⎝ ⎠ This expression is in the form of the equation of a straight line through the origin, y gradient x = × [Turn over 3 Page 36 MARKS DO NOT WRITE IN THIS MARGIN 16. (b) (continued) The student measures the height of the slope h. The student then allows the sphere to roll down the slope and measures the final speed of the sphere v at the bottom of the slope as shown in Figure 16. data logger not to scale Figure 16 light gate height of slope, h The following is an extract from the student’s notebook. h (m) v (m s−1) 2gh (m2 s−2) v2 (m2 s−2) 0·020 0·42 0·39 0·18 0·040 0·63 0·78 0·40 0·060 0·68 1·18 0·46 0·080 0·95 1·57 0·90 0·100 1·05 1·96 1·10 m = 3·8 kg r = 0·053 m (i) On the square-ruled paper on Page 37, draw a graph that would allow the student to determine the moment of inertia of the sphere. (ii) Use the gradient of your line to determine the moment of inertia of the sphere. Space for working and answer 3 3 Page 37 (An additional square-ruled paper, if required, can be found on Page 42.) [Turn over for next question Page 38 MARKS DO NOT WRITE IN THIS MARGIN 16. (continued) (c) The student states that more confidence should be placed in the value obtained for the moment of inertia in the second method. Use your knowledge of experimental physics to comment on the student’s statement. [END OF QUESTION PAPER] 3 Page 39 MARKS DO NOT WRITE IN THIS MARGIN ADDITIONAL SPACE FOR ANSWERS AND ROUGH WORK Additional diagram for Question 2 (b) (ii) r Figure 2C ω Additional diagram for Question 5 (b) (i) A B spacecraft accelerating in this direction Figure 5A Page 40 MARKS DO NOT WRITE IN THIS MARGIN ADDITIONAL SPACE FOR ANSWERS AND ROUGH WORK Additional diagram for Question 5 (b) (ii) spacecraft moving at a constant speed A B Figure 5B Additional diagram for Question 7 (b) (ii) 0 500 1000 1500 2000 λ (nm) Intensity curve A curve B Figure 7 Page 41 MARKS DO NOT WRITE IN THIS MARGIN ADDITIONAL SPACE FOR ANSWERS AND ROUGH WORK Additional diagram for Question 10 (c) (ii) time 0 displacement from equilibrium position Additional diagram for Question 13 (b) (iii) Q2 Q1 Figure 13C Page 42 Page 43 MARKS DO NOT WRITE IN THIS MARGIN ADDITIONAL SPACE FOR ANSWERS AND ROUGH WORK Page 44 MARKS DO NOT WRITE IN THIS MARGIN ADDITIONAL SPACE FOR ANSWERS AND ROUGH WORK