IB DP Physics HL Unit 1. Measurements and uncertainties Question Bank paper 1

Question

What are the units of specific energy and energy density?

 

Specific energy

Energy density

A.

J m–1

J m–2

B.

J kg–1

J m–3

C.

J kg–1

J m–2

D.

J m–1

J m–3

Answer/Explanation

Ans: B

Specific energy or massic energy is energy per unit mass. The SI unit for specific energy is the joule per kilogram (J/kg).

Energy density is the amount of energy stored in a given system or region of space per unit volume. SI unit J/m3

Question

Two lengths, \(a\) and \(b\), are measured to be \(51 \pm 1{\text{ cm}}\) and \(49 \pm 1{\text{ cm}}\) respectively. In which of the following quantities is the percentage uncertainty the largest?

A.     \(a + b\)

B.     \(a – b\)

C.     \(a \times b\)

D.     \(\frac{a}{b}\)

Answer/Explanation

Ans.

B

\(a+b=100\pm 2 \;cm\) so the percentage error is 2/100= 2%
\(a-b=2\pm 2 \; cm\) so the percentage error is 2/2= 100%
The percentage errors for a and b separately are 1/51= 0.0196 or about 2% and 1/49= 0.02041 or about 2%

so the percentage errors of a x b and a/b are 2+ 2= 4%

 

Question

Which of the following expresses the units of capacitance in terms of fundamental units?

A. \({{\rm{s}}^{\rm{4}}}{{\rm{A}}^{\rm{2}}}{{\rm{m}}^{{\rm{ – 2}}}}{\rm{k}}{{\rm{g}}^{{\rm{ – 1}}}}\)

B. \({{\rm{s}}^{\rm{2}}}{\rm{A}}{{\rm{m}}^{{\rm{ – 2}}}}{\rm{k}}{{\rm{g}}^{{\rm{ – 1}}}}\)

C. \({{\rm{s}}^{\rm{4}}}{{\rm{A}}^{\rm{2}}}{{\rm{m}}^{{\rm{ – 2}}}}\)

D. \({{\rm{s}}^{\rm{2}}}{\rm{A}}{{\rm{m}}^{{\rm{ – 2}}}}\)

Answer/Explanation

Ans:

A

A farad is a derived unit based on four of the seven base units of the International System of Units: kilogram (kg), metre (m), second (s), and ampere (A).

\(C=\frac{Q}{V} =\frac{Q}{\frac{W}{Q}}=\frac{Q^2}{W}\)

\(=\frac{(It)^2}{F\times d} =\frac{I^2t^2}{m\times a\times d}\)

\(=\frac{A^2s^2}{kg\times m\times s^{-2}\times m}\)

\(=s^4A^2 m^{-2}kg^{-1}\)

Question

The volume V of a cylinder of radius R and height H is given by V = \(\pi \)R2H. The volume of the cylinder was measured with an uncertainty of 10% and the height was measured with an uncertainty of 6%. What is the uncertainty in the radius of the cylinder?

A. 1%
B. 2%
C. 4%
D. 8%

Answer/Explanation

Ans.

D

\(V=\pi R^2H \)
\(R^2 =\frac{V}{\pi H}\)

The rule of dealing with uncertainties in mathematical calculations;

• you add percentage uncertainties when you multiply or divide quantities.

• if a quantity is squared you double the uncertainty, if cubed it is 3 times etc. i.e. multiply by the index. Square root is index half so divide by 2.

Uncertainty in R  will be \(\frac{10+6}{2}=8%\)