# 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

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.     $$\frac{a}{b}$$

### 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. $${{\rm{s}}^{\rm{2}}}{\rm{A}}{{\rm{m}}^{{\rm{ – 2}}}}$$

### 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%

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 $$\frac{10+6}{2}=8%$$