Edexcel A-Level Physics A2 6.5.10 Compound Percentage Uncertainties Questions

Review compound percentage uncertainties in Edexcel A-Level Physics through measured quantities, powers and combined uncertainty calculations.

Exam points

combine percentage uncertainties in compound terms with repeated powers such as D² and d²

[Maximum number: 3]

A student added small lead spheres to a test tube. The student placed the test tube in a small beaker of water. The test tube floated as shown.

Figure for Question Edexcel A-Level Physics A2 6.5.10 Compound Percentage Uncertainties Questions question 1 — Edexcel A-Level Physics A2

The student gave the test tube a small vertical displacement. The test tube then oscillated vertically.

The student replaced the water with another liquid. The period is given by $T=\sqrt{\frac{16\pi m}{D^2\rho g}},$ where D is the test-tube diameter, m is the mass of the test tube and spheres, and $\rho$ is the liquid density.

Show that the percentage uncertainty in $\rho$ is about $4\%$ .

Because $\rho\propto D^{-2}T^{-2}$ , $%U(\rho)=2\frac{0.01}{2.38}\times100+2\frac{0.01}{0.61}\times100=4.12\%,$ about $4\%$ .

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Edexcel A-Level Physics A2 6.5.10 Compound Percentage Uncertainties Questions question 1