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 uncertainty in R is ΔR.

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

A  \(\frac{2\Delta R}{R}\)

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 Area  \(A=\pi R^2\)

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 and  \(\Delta r\) 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

λ

±10 %

Y

±0.05 %

z

± 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 %