TJC 2024 H2 Paper 4 Solutions

Name: _____________________________________ CG: ___________ Date: _____________ Marking Scheme for Question 1 No Mark Scheme Mark Score 1(a) d measured to the nearest 0.01 mm with consistent unit Evidence of repeated measurements of d 1 (b) A calculated correctly to correct s.f 1 (e) I recorded to the nearest 0.1 mA with consistent unit. V1 and V2 recorded to the nearest 0.001 V 1 1 (f) Tabulate at least 6 sets of readings with correct d.p for I, V1 and V2. Award 0 marks if < 5 readings are taken. Award 0 marks if assistance is provided in circuit setup. Correct d.p for V1 + V2 Correct column headings with units Note: − 2 marks for table if unable to obtain varying I, V1 and V2 values. 1 1 1 (g) Graph Correct linearization equation. Note: (V1 + V2) against I Correct label of axes and graph should occupy at least half of graph paper. Correct plotted points Gradient coordinates read correctly and correct calculation of gradient. Correct calculation of  with units. 1 1 1 1 1 (i) Sensible method to obtain ratio of cross-sectional areas. e.g. ratio of 1 2 V V . 1 Total 13

No Marking Instructions Mark Score 2(b)(i) L and a recorded to nearest mm or 1 dp in cm or 3 dp in m. 1 2(b)(ii) b recorded to nearest mm or 1 dp in cm or 3 dp in m. b should be between 70 % to 90 % of a Repeat measurement 1 1 2(c)(i) Acceptable explanation 1 2(c)(ii) Uncertainty in b greater than 0.2 cm Percentage uncertainty to 2 sf 1 2(d) K calculated correctly to 3 sf 1 2(e) Correct linearization of eqn Correct expression for gradient 1 1 Total 8

No Marking Instructions Mark Score 3(a)(i) D recorded to nearest 0.01 cm with unit Zero error recorded or evidence of repeat measurement (range of D is with 10%) 1 (a)(ii) d recorded to nearest 0.01 cm with unit. Evidence of repeat measurement 1 (a)(iii) r calculated correctly to correct d.p. with unit 1 (a)(iv) Correct calculation of % uncertainty using sensible value of D and x. (0.03 cm ≤D andx ≤ 0.05 cm) 2 (b)(i) TR calculated correctly to 3 sf with clear working from <t> 1 (b) (ii) TS calculated correctly to 3 sf with clear working from <t>, TS > TR 1 (c) L recorded to the correct d.p. with unit . Evidence of repeat measurement TR calculated correctly to 3 sf with clear working from <t> TS calculated correctly to 3 sf with clear working from <t> (*value of TS larger than TR , otherwise minus 1 mark) 2 (d)(i) Correct calculations of the two k values with correct unit 1 1 (d)(ii) Correct justification of s.f. of k linked to s.f. in r, L and TR (lowest s.f.) 1 (d)(iii) Draw conclusion based on stated criterion. (e.g. not obeyed because % difference of k values > % uncertainty of r in (a)(iii)) 1 (e) (i) All observations plotted and line of best fit is drawn 1 (e)(ii) Linearising equation and deriving gradient/y-intercept of graph Gradient – hypotenuse of the triangle is greater than half the length of the drawn line. Read-offs must be accurate to half a small square Value of n calculated correctly using gradient 1 1 1 (f) Correct method to locate the centre of the discs accurately Basic procedure and method of measuring period and r Control of variable : Keep L constant at the 3 positions of disc with the help of a metre rule Correct graph to plot How the graph shows that T is inversely proportional to r 1 1 1 1 1 Total 22

Suggested mark scheme for question 4 : Marks A1 Design (1 A mark) Diagram with method to produce sound (using loudspeaker connected to signal generator) and CRO to measure frequency and amplitude of reflected sound (and incident sound) B1 B2 B3 B4 B5 Procedure (5 B Marks) Method of determining the density; measuring mass of foam (mass balance) and dimensions of foam (vernier calliper or micrometer, accept ruler) Method of measuring the frequency of transmitted sound (f =1/T where T from time-base on CRO; time base setting x no. of div for 1 complete wave shown on CRO.) Method of measuring the intensity of transmitted sound; Measure amplitude from vertical sensitivity on CRO; height × y-gain and determine the intensity of sound; IAmplitude2 Method to vary the frequency of sound (by varying frequency on signal generator) Method to vary foam ; replace with another foam of different density. C1 C2 C3 C4 Safety and Analysis (4 C marks) Expt 1 : constant  , Plot lg I vs lg f , gradient = m, y-intercept = lg (P n) Expt 2 : constant f, Plot lg I vs lg  , gradient = n, y-intercept = lg (P fm) Obtain P from intercept of Expt 1: 10 y-intercept = A n Or from Expt 2: 10 y-intercept = A fm (Need to show fully linearised equation to get the mark) lg I =m lg f +n lg  + lgP Precaution linked to loud sounds e.g. use ear plugs/muffs. D1 D2 D3 D4 D5 Details (Max 2 D marks) The experiment conducted in a quiet room or soundproof enclosure to reduce background noise/ensure no other background noise. Do a pre-experiment to select an appropriate volume of sound that will be comfortably detected/measurable by the CRO Keep position and angle between loudspeaker and foam constant, as well as position and angle between microphone and foam constant by measuring regularly, using a metre ruler / making markings and checking angles to ensure they are always constant. 90° angle to be avoided Keep amplitude of incident sound constant by not changing the setting on the signal generator and to ensure it is constant by measuring it using a sound intensity meter/checking the amplitude using the vertical displacement on the CRO regularly. Other possible good physics suggestions 12

Experimental data and suggested solutions for Question 1 1(a) Zero error = 0.00 mm ' 1 '' 1 0.32 mm 0.32 mm 0.32 mm d d d = = = 1(b) 23 8 8 2 1 0.32 10 8.04 10 8.0 10 m2A  − −− = =  =   1(c) Zero error = 0.00 mm ' 2 '' 2 2 0.46 mm 0.46 mm 0.46 mm d d d = = = 23 7 7 2 2 0.46 10 1.66 10 1.7 10 m2A  − −− = =  =   1(e) 1 2 41.3 mA 0.115 V 0.101 V V V = = = I 1(f) I/ mA V1 / V V2 / V (V1 + V2) / V 41.3 0.115 0.101 0.216 42.6 0.119 0.104 0.223 47.3 0.133 0.117 0.250 55.3 0.153 0.135 0.288 64.5 0.180 0.158 0.338 92.3 0.257 0.225 0.482 1(g)

Gradient of graph = 112 12 0.0052 V/mA = 5.2 V A yy xx −− =− Gradient of graph = L AA12 11 +   2 87 11(35 10 ) 5.2 8.04 10 1.66 10  − −−  + =    = 8.05 x 10−7  m 1(h) The ratio 1 2 V V gives the ratio of the cross-sectional areas 2 1 A A . (Since current is constant, V = IR =I L A . The voltage across wire V is inversely proportional to cross -sectional area. Hence the ratio of cross -sectional area can be obtained from voltmeter readings.) 2(b)(i) a = 25.0 cm 2(b)(ii) b = 20.7 cm 2(c)(i) Use of fiducial marker Repeated observations to refine position Or anything that is reasonable 2(c)(ii) 0.5 / 20.7  100% = 2.4% y = 0.0052x + 0.0017 0.2 0.25 0.3 0.35 0.4 0.45 0.5 40 50 60 70 80 90 100 (V1+V2)/V I / mA

2(d) k = (50.0 – (50.02 − 20.72)1/2) / (50.0 – (50.02 − 25.02)1/2) = 0.670 2(e) 22 22 L L bk L L a −−= −− −−− − = 22 22 L L bL L a k −−− = − + 22 22 L L bL a L k Plot a graph −22La vs −− 22L L b to get a straight line With gradient = 1/k so k = 1/gradient Question 3 Suggested solution (a)(i) =zero error 0.00 cm D =1 15.00 cm , D =2 14.80 cm ( )D D D= + =1 122 14.90 cm (a)(ii) 1 0.21 cm=d , 2 0.27 cm=d , 3 0.27 cm=d ( )1 1 2 33 0.25 cm= + + =d d d d (a)(iii) r D x= − =  − =11 22 14.90 0.25 7.20 cm (a)(iii) Measure distance x of one hole from its nearest edge of the disc with vernier callipers. Repeat for the