# IBDP Physics Unit 1.2 Uncertainties and errors HL Paper 1

### Question

A student measures the radius R of a circular plate to determine its area. The absolute uncertaintyÂ in R is Î”R.

What is the fractional uncertainty in the area of the plate?

AÂ  $$\frac{2\Delta R}{R}$$

B $$(\frac{\Delta R}{R})^2$$

C $$\frac{2\pi \Delta R}{R}$$

D $$\pi (\frac{\Delta R}{R})^2$$

Answer/Explanation

Ans: A

For calculating approximate uncertainty we proceed as follows:

We know that AreaÂ  $$A=\pi R^2$$

Taking natural log on both sides we get

$$ln A=ln(\pi \times r^2)$$
$$ln A= ln \pi + 2ln r$$

From Theory of errors we can write it as
$$\frac{\Delta A}{A} =\frac{2\Delta r}{r}$$

where $$\Delta A$$ is uncertainty in A andÂ  $$\Delta r$$ is uncertainty in r , there being no uncertainty in constant $$\pi$$

### Question

A student is verifying the equation

$$x=\frac{2\lambda y}{z}$$

The percentage uncertainties are:

 Quantity Uncertainty Î» Â±10 % Y Â±0.05 % z Â± 5 %

What is the percentage uncertainty in x?

A 5 %

B. 15 %

C. 25 %

D. 30 %

Answer/Explanation

Ans: B

Hence percentage uncertainty in x = 10+5+0.05 = 15 %