A student measured a metal ring of the type shown below - Edexcel - A-Level Physics - Question 4 - 2023 - Paper 6

To calculate the mean value of d:

Mean of d = \frac{8.53 + 8.56 + 8.55 + 8.53}{4} = \frac{34.17}{4} = 8.54 , \text{mm}

For the uncertainty, we calculate the uncertainty based on the variation: Uncertainty = \frac{(8.56 - 8.53)}{2} = 0.015 , \text{mm}

So, the mean value of d is 8.54 mm ± 0.02 mm.

Using the formula for the uncertainty in a squared measurement:

[ U_{d^{2}} = d \times U_{d} \times 2 ]

If d = 10.70 mm with an uncertainty of 0.06 mm, we calculate:

[ U_{d^{2}} = 10.70 , \text{mm} \times 0.06 , \text{mm} \times 2 \approx 1.28 , \text{mm}^2 ]

This shows that the uncertainty in d² is approximately 1 mm².

To find the percentage uncertainty in the area A:

Percentage uncertainty = \left( \frac{U_A}{A} \right) \times 100 %

Assuming the area A has a calculated uncertainty of 2.4 mm², and using A = 602 mm², we get:

[ \frac{2.4}{602} \times 100 \approx 0.4 % ]

This shows that the percentage uncertainty in A is about 0.4%.

Measuring the total mass of 10 metal rings reduces the impact of random errors that may arise from single measurements. The averaging of these measurements tends to yield a more reliable and accurate representation of the mass per ring, accounting for variations in the weighing process due to calibration or environmental factors.

To find the mean density ρ₁:

First, convert the total mass to grams and total volume to cubic centimeters:

Using the formula:

[ \rho = \frac{m}{V} ]

Where m = total mass = 63.0 g and V = total volume derived from thickness and area.

The density is calculated with:

[ V = A \times x_{0} ]

After that, substitute the values to find the mean density.

Given the density ranges from 7.48 g cm⁻³ to 7.95 g cm⁻³, if our calculated density lies within this range, we can deduce that the metal rings could be made from stainless steel.