IB PHYSICS HL(Higher level) – 2024 – Practice Questions- All Topics
Topic 1.1 Measurement in Physics
Topic 1 Weightage : 7 %
All Questions for Topic 1.1 – SI units, calculations and presentation of raw and processed data, scientific notation and metric multipliers, Quoting and comparing ratios, values and approximations to the nearest order of magnitude. Significant figures, Orders of magnitude, Estimation
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
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%
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 \(\frac{10+6}{2}=8%\)