(a) Table 1.1 lists some SI quantities. Complete the table by indicating with a tick (✓) which rows are SI base quantities. (1 mark)
(b) Use the definition of power to determine its SI base units. (2 marks)
SI base units = ________________________________________________
(c) A light meter is used to measure the intensity of light in a classroom. Daylight is incident normally on the sensor of the meter. The sensor has an area of \(2.2\,\mathrm{cm^2}\). The reading on the meter is \(950\,\mathrm{W\,m^{-2}}\).
Calculate the power of the daylight incident on the sensor. (3 marks)
power = ________________________________________________ \( \mathrm{W} \)
Syllabus Topic Codes (Cambridge International AS & A Level Physics 9702):
(a) SI base quantities [1 mark]
The SI base quantities listed in the table are current and mass.
Therefore, the table should be completed as follows:
| Quantity | Base quantity |
|---|---|
| Current | ✓ |
| Energy | |
| Force | |
| Mass | ✓ |
Answer: Current and mass
(b) SI base units of power [2 marks]
Power is defined as the rate of doing work:
\( P=\frac{W}{t} \)
The SI unit of work is the joule, so:
\( \mathrm{unit\ of\ power}=\mathrm{J\,s^{-1}} \)
Since:
\( \mathrm{J}=\mathrm{kg\,m^2\,s^{-2}} \)
Therefore:
\( \mathrm{J\,s^{-1}}=\mathrm{kg\,m^2\,s^{-2}\,s^{-1}} \)
\( \mathrm{J\,s^{-1}}=\mathrm{kg\,m^2\,s^{-3}} \)
Answer: \( \boxed{\mathrm{kg\,m^2\,s^{-3}}} \)
(c) Power of daylight incident on the sensor [3 marks]
The intensity is power per unit area:
\( I=\frac{P}{A} \)
Rearranging:
\( P=IA \)
The sensor area must be converted from \(\mathrm{cm^2}\) to \(\mathrm{m^2}\):
\( A=2.2\,\mathrm{cm^2}=2.2\times10^{-4}\,\mathrm{m^2} \)
Using \(I=950\,\mathrm{W\,m^{-2}}\):
\( P=(950)(2.2\times10^{-4}) \)
\( P=0.209\,\mathrm{W} \)
To an appropriate number of significant figures:
\( P=0.21\,\mathrm{W} \)
Answer: \( \boxed{0.21\,\mathrm{W}} \)
