Questions
PHYSICS PAPER III (ALTERNATIVE A)
1A. The concentration C of a chemical tracer in a solution decreases with time according to:
C = C₀e^(−kt) ...(1)
where C₀ and k are constants.
| t/min | 0.18 | 0.22 | 0.24 | 0.27 | 0.30 | 0.34 | 0.39 | 0.45 | 0.57 | 0.65 |
|---|---|---|---|---|---|---|---|---|---|---|
| C/mg·L⁻¹ | 13.60 | 11.75 | 10.50 | 9.15 | 8.30 | 7.10 | 5.95 | 4.80 | 3.60 | 2.85 |
i. Transform equation (1) into a straight-line form to determine C₀ and k.
ii. Form a composite table containing all necessary parameters to determine C₀ and k graphically.
iii. Use your graph to determine the approximate values of C₀ and k.
iv. From the graph, find the approximate value of C when t = 0.38 minutes.
v. From your values of C₀ and k, use equation (1) to find the value of t when C = 6.75 mg·L⁻¹.
b. If m = 1.8 ± 0.003 and n = 2.89 ± 0.0011, find the error in determining the value of the term m² + √n.
2A. Hang a single spiral spring of known elastic constant from a rigid support as shown in Figure 1 with M = 60 g. Displace the spring vertically downward through a small distance and gently release it. The spring performs simple harmonic oscillations. With the help of a stopwatch, record the time for 25 complete oscillations. Find the time period T. Evaluate T². Repeat the experiment for five other different values of M within the elastic limit.
i. Tabulate your readings.
ii. Plot a graph of T² against M. Find the slope S of the graph.
iii. If T = 2π√(M/k), use your slope to find the value of k.
iv. State two precautions taken to ensure accurate results.
3A. Use the diagram in Figure 2.1 to carry out the following instructions. For the ray FGHJ, the angle of incidence is i and the angle of emergence is θ.
i. Trace the outline of a triangular glass prism DEF. Set the angle of incidence i = 20°. With the help of optical pins, find the angle of emergence θ.
ii. Measure and record the corresponding angle marked 'b'. Evaluate sin θ and sin b.
iii. Repeat the experiment with i = 25°, 35°, 40°, 45° and 50° respectively.
iv. Prepare a composite table for your readings. Plot a graph of sin b against sin θ. Find the slope S of the graph and evaluate S⁻¹.
v. State two precautions taken to ensure accurate results. Attach the traces to your answer booklet.
b. Assume the angle of a triangular glass prism of refractive index 1.52 is approximately 60°. Find the angle of minimum deviation.
Solutions
1A i. Taking natural log of both sides of C = C₀e^(−kt):
ln C = ln C₀ − kt
Plotting ln C (y-axis) against t (x-axis) gives a straight line with slope = −k and y-intercept = ln C₀.
1A ii. Composite table:
| t/min | 0.18 | 0.22 | 0.24 | 0.27 | 0.30 | 0.34 | 0.39 | 0.45 | 0.57 | 0.65 |
|---|---|---|---|---|---|---|---|---|---|---|
| C/mg·L⁻¹ | 13.60 | 11.75 | 10.50 | 9.15 | 8.30 | 7.10 | 5.95 | 4.80 | 3.60 | 2.85 |
| ln C | 2.61 | 2.46 | 2.35 | 2.21 | 2.12 | 1.96 | 1.78 | 1.57 | 1.28 | 1.05 |
1A iii. Slope using end points (0.18, 2.61) and (0.65, 1.05):
slope = (1.05 − 2.61)/(0.65 − 0.18) = −1.56/0.47 ≈ −3.32 min⁻¹
So k ≈ 3.32 min⁻¹
Intercept: ln C₀ = 2.61 + 3.32(0.18) = 3.21 → C₀ = e^3.21 ≈ 24.8 mg·L⁻¹
1A iv. At t = 0.38: ln C = 3.21 − 3.32(0.38) = 1.95 → C = e^1.95 ≈ 7.03 mg·L⁻¹
1A v. C = 6.75: ln(6.75) = 1.91
1.91 = 3.21 − 3.32t
t = 1.30/3.32 ≈ 0.39 min
b. m² = 3.24, d(m²) = 2m·dm = 2(1.8)(0.003) = 0.0108
√n = 1.70, d(√n) = dn/(2√n) = 0.0011/3.40 = 0.00032
z = m² + √n = 4.94
dz = d(m²) + d(√n) = 0.0108 + 0.0003 = 0.0111
z = 4.94 ± 0.011
2A i–ii. (Requires actual lab readings: time 25 oscillations at 6 values of M, compute T = time/25, then T², plot T² vs M.)
2A iii. T² = 4π²M/k → slope S = 4π²/k
k = 4π²/S
2A iv.
- Avoid parallax error when reading the position of the pointer/reference mark against the scale.
- Ensure the spring oscillates only in the vertical plane, avoiding sideways swinging that would affect timing.
3A i–iv. (Requires actual ray-tracing readings for each i; tabulate i, θ, b, sin θ, sin b; plot sin b vs sin θ; slope S and S⁻¹ read from graph.)
3A v.
- Use sharp pencils and well-separated optical pins to reduce parallax error in sighting the ray.
- Hold the prism firmly in place so its outline does not shift while tracing the rays.
3A b. n = sin[(A+D)/2] / sin(A/2)
1.52 = sin[(60+D)/2] / sin 30°
sin[(60+D)/2] = 1.52 × 0.5 = 0.76
(60+D)/2 = sin⁻¹(0.76) ≈ 49.46°
60 + D = 98.92°
D ≈ 38.9°