2021 H2 Prelim Phy P4 MS

Mark Scheme for Practical Qn Marking Point Marks 1(a)(i) Raw L to the nearest 0.1 cm and final value in the range 11.5–12.5 cm. 1 1(a)(ii) Percentage uncertainty based on an absolute uncertainty ΔL in the range 2–5 mm. If repeat readings have been taken, then the absolute uncertainty can be half the range (but not zero) if the working is clearly shown. Correct method of calculation to obtain percentage uncertainty. 1 1(b)(i) All raw times measured either to the nearest 0.1 s or all to the nearest 0.01 s. Evidence of measurement of nT repeated where nT ⩾ 10.0 s. Value of T in the range 0.5 s ⩽ T ⩽ 1.0 s. 1 1 1 1(b)(ii) Calculation of T2 correct. 1 1(b)(iii) Justification of the number of significant figures in terms of the number of s.f. in (raw) time only. 1 1(c)(i) Raw L to the nearest 0.1 cm and final value in the range 5.5–6.5 cm. 1 1(c)(ii) Second value of T < first value of T. 1 1(d)(i) Calculated correctly two values of k with unit and recorded to the least no. of sf among T and L. The final k values must not be fractions. Unit: cm0.5 s-1 or equivalent 1 1 1(d)(ii) Justification of Relationship Note: The given relation is valid for a compound pendulum.  Calculated correctly %kuncertainty = ∆ k kave x 100% OR %kuncertainty = ∆ k ksmaller x 100%  ∆ k=|k1 - k2 | OR ∆ k =|k1 - k2 |/2  Chose a criterion from the value in (a)(ii).  Concluded that results do not support the suggestion if %kuncertainty > the criterion chosen. OR Concluded results support the suggestion if %kuncertainty  the criterion chosen. (Expected) 1 1 1(e) Correct calculation of g using candidate’s second k and in range 9.0 m s-2 ⩽ g ⩽ 11.0 m s-2. 1 Fig. 1 Excel-Generated Theoretical Table for Q1 For internal use only DHS2021 1

Total 14 For internal use only DHS2021 2

Qn Marking Point Marks 2(a) R measured while resistor is in operation i.e., 1 Value of RA, RB and RC with unit in the range 64 - 72 Ω. 1 Fig. 2a Excel-Generated Theoretical Table for Q2a 2(b)(i) Value of I with unit in the range 30.0–50.0 mA. 1 2(c) Seven sets of readings of R: 22.7 Ω, 34.0 Ω, 45.3 Ω, 68.0 Ω, 102 Ω, 136 Ω & 204 Ω Six sets of readings of R 2 or 1 Column headings: Each column heading must contain a quantity, a unit, and a separating mark where appropriate. The presentation of quantity and unit must conform to accepted scientific convention, e.g. R / Ω, I / mA and . 1 Consistency of presentation: All raw values of I must be given to 0.1 mA or all to 0.01 mA. 1 Significant figures: All values of must be given to the same number of s.f. as the number of s.f. in raw I. Calculation: Values of are correct. 1 For internal use only DHS2021 3

Fig. 2b Excel-Generated Theoretical Table for Q2c 2(d) Stated appropriate graph to be plotted. 1 E is determined by the inverse of the gradient. X is determined by product of y-intercept and E. 1 Total 10 For internal use only DHS2021 4

Qn Marking Point Marks 3(a) Value of S with unit in the range 4.50 – 5.50 cm. 1 3(b)(iii) Measurement and Observation Recorded two values of S1 and two values of S2, and their averages to nearest 0.001 m (i.e., 0.1 cm). 1 3(b)(iv) p and q calculated correctly, and recorded to nearest 0.001 m (i.e. 0.1 cm). 1 3(c) Six (or more) sets of readings of m, including m = 100 g and m = 400 g 1 Column headings: Each column heading must contain a quantity, a unit, and a separating mark where appropriate. The presentation of quantity and unit must conform to accepted scientific convention, e.g. m / g, S1 / cm, S2 / cm, p / cm, q / cm, mg / N and . 1 Consistency of presentation: All raw values of S1 and S2 must be given to 0.1 cm. All raw values of m must have no d.p. in g. 1 Decimal places: All values of p and q must be given to the same number of d.p. as the number of d.p. in raw S1 and S2 respectively. Significant figures: All values of mg must be given to the same number of s.f. as the number of s.f. in raw m. All values of must be given to the least no. of s.f. among p and q Calculation: Values of mg and are correct. 1 Fig. 3 Excel-Generated Theoretical Table for Q3c For internal use only DHS2021 5

3(d) (GRAPH) ● Sensible scales must be used. Awkward scales (e.g., 3:10) are not allowed. Scales must be chosen so that plotted points occupy at least half the graph grids in both x and y directions. ● Axes must be labelled with the quantity which is being plotted. 1 ● Straight line of best fit- judge by scatter of points about the candidate's line. No curved lines allowed. ● There must be an even distribution of points on either side of the line along the full length. ● Allow maximum (correctly identified) one anomalous point if clearly indicated on graph i.e., circled or labelled. There must be at least five points left after the anomalous point is disregarded. ● Lines must not be kinked or thick. No hairy lines. (No curved lines allowed). 1 All observations in table must be plotted. Work to an accuracy of plot ≤ 0.5 small square. 1 3(d) (CALN) ● Equation linearised correctly. ● Plot a sensible graph that allows for straight line to be drawn and k to be determined from the gradient. e.g. mg / N vs . 1 ● Gradient calculated correctly with clear working. ● The hypotenuse of the gradient triangle must be greater than half the length of the drawn line. ● Read-offs must be accurate to half a small square. 1 ● k determined correctly from gradient with unit. 1 3(e) Comments on whether there are any anomalous data - with the anomalous data clearly identified e.g., “There are no anomalous points as all plotted points are evenly distributed on both sides of the best fit line and no point is significantly further from the best fit line compared to other points.” Justifies whether there is any anomalous data based on deviation of the points from the linear trend e.g., “Point (4.300, 7.00) is an anomalous point because point (4.300, 7.00) is significantly further from the best fit line as compared to other points.” 1 3(f)(i) Difficult to measure angle with reason e.g., hand shakes / curve at bottom / position of zero uncertain / parallax / holding set square without a stand 1 3(f)(ii) Trace on a card / use graph paper / project onto screen and measure angle / use trigonometry / take photo and measure angle / clamp set square 1 For internal use only DHS2021 6

3(g) Fig. I (a) Measure the provided masses, m’ using an electronic balance and labelled them. (b) Measure the natural length of spring CD, L’0 using a metre ruler. (c) Set up the apparatus as shown in Fig. I. (d) Record the known mass m’. (e) Record the angle using a protractor while keeping AB horizontal. (f) Record the length L’ using a metre ruler. Ensure it is constant. (g) Repeat steps (d), (e) and (f) while varying the mass of the load m’ to obtain 5 additional sets of readings. (h) Resolving forces vertically, where is the tension in spring CD and is the acceleration of freefall. Plot a graph of against , which is a straight-line graph through the origin with gradient is the gradient. (i) [1] for diagram [1] control of variables [1] for process and how to determine k Total 19 For internal use only DHS2021 7 Length of Spring, L’ Mass of Load, m’

Qn Marking Point Marks 4 Mark Scheme Defining the problem A1: identify independent (frequency f of light, thickness of glass t) and dependent (ratio A/A0) variables A2: identify control variable (e.g. keep distance between light source and sensor constant) 1 1 Method of data collection B1: labelled diagram showing a setup of laser, glass block(s) and light sensor in a line B2: method to determine the different frequencies of laser (e.g. using diffraction grating and nλ = d sin θ B3: method to determine thickness of glass t, using vernier calipers or metr