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#	Question	Answer
1	What are derived units?	Units of physical quantities obtained by combining the base units.
2	What are significant figures?	The reliable digits plus the first uncertain digit in a measured value.
3	Are trailing zeros in a number without a decimal point significant?	No.
4	What is the rule for rounding off when the digit to be dropped is 5 and the preceding digit is even?	The insignificant digit is simply dropped and the preceding digit is left unchanged.
5	What is a dimensional formula?	The expression which shows how and which of the base quantities represent the dimensions of a physical quantity.
6	Can the method of dimensions determine the value of a dimensionless constant?	No.
7	What is the volume of a cube of side 1 cm in m³?	\( 10^{-6}\,\mathrm{m^3} \).
8	What is the value of 1 angstrom in metres?	\( 1\,\mathrm{\AA} = 10^{-10}\,\mathrm{m} \).
9	What are the base units for length, mass and time in the FPS system?	Foot, pound and second respectively.
10	How many seconds are there in one year (1 y = 365.25 d)?	\( 3.156 \times 10^{7}\,\mathrm{s} \).
11	What is 1 degree equal to in radians?	\( 1^\circ = (\pi/180)\,\mathrm{rad} \).
12	What is meant by the order of magnitude of a physical quantity?	The power \( b \) of 10 when the quantity is expressed approximately as \( 10^b \) (rounding the coefficient to 1 for \( a \le 5 \) and to 10 for \( 5 < a \le 10 \)).
13	Each side of a cube is measured to be 7.203 m. What is its volume to appropriate significant figures?	\( 373.7\,\mathrm{m^3} \) (7.203³ rounded to 4 significant figures).
14	If length \( l = 16.2 \pm 0.1\,\mathrm{cm} \) and breadth \( b = 10.1 \pm 0.1\,\mathrm{cm} \), what is the area \( lb \) with its uncertainty?	\( lb = 164 \pm 3\,\mathrm{cm^2} \) (combining the percentage errors of \( l \) and \( b \)).
15	What are the dimensions of velocity or speed?	\( [L T^{-1}] \), or \( [M^0 L T^{-1}] \).
16	What must be true of the arguments of trigonometric, logarithmic, and exponential functions?	They must be dimensionless.
17	Is the equation \( \frac{1}{2} m v^2 = m g h \) dimensionally correct?	Yes, both sides reduce to \( [M L^2 T^{-2}] \).
18	Which is the most precise device for measuring length: a vernier calipers with 20 divisions, a screw gauge of pitch 1 mm with 100 divisions, or an optical instrument that measures to within a wavelength of light?	The optical instrument, since the wavelength of light (~10⁻⁷ m) is far smaller than the least count of the vernier calipers (~5 × 10⁻⁵ m) or the screw gauge (~10⁻⁵ m).
19	Given the Sun's mass is \( 2.0 \times 10^{30}\,\mathrm{kg} \) and radius \( 7.0 \times 10^{8}\,\mathrm{m} \), in what density range does the Sun's mass density fall, despite being a hot plasma?	About \( 1.4 \times 10^{3}\,\mathrm{kg\,m^{-3}} \), which falls in the range of densities of solids and liquids rather than typical gases, due to the Sun's enormous gravitational compression.
20	What fixed numerical value of the Boltzmann constant \( k \) is used to define the SI kelvin?	\( 1.380649 \times 10^{-23}\,\mathrm{J\,K^{-1}} \), which is equal to \( \mathrm{kg\,m^2\,s^{-2}\,K^{-1}} \).
21	How many significant figures does 123 m (= 12300 cm = 123000 mm) have?	Three; the trailing zeros are not significant since there is no decimal point.
22	A screw gauge has a pitch of 1.0 mm and 200 divisions on the circular scale. Can its accuracy be increased arbitrarily by increasing the number of divisions?	No; beyond a certain point, practical limitations such as structural flexibility of the screw prevent further improvement in accuracy.