UNITS AND MEASUREMENT
Frequently Asked Questions
A physical quantity is a property of a system that can be measured and expressed numerically with a unit, such as length, mass, and time.?
A unit is a standard reference chosen to measure a physical quantity, e.g., metre for length, kilogram for mass.?
Physical quantities that are independent of other quantities, e.g., length, mass, time, electric current, temperature, amount of substance, luminous intensity.?
There are seven SI base quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance, luminous intensity.?
Metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd).?
Quantities defined using base quantities (e.g., velocity, force); their units are combinations of base units (e.g., \(m\ s^{-1},\ kg\ m\ s^{-2}\).?
SI supplementary units are: radian (rad) for plane angle and steradian (sr) for solid angle.?
It is internationally accepted, coherent, and based on seven base units with well-defined standards, simplifying scientific communication.?
A system where derived units are obtained from base units without additional numerical factors, e.g., \(1\ N = 1\ kg\ m\ s^{-2}\).?
It is the expression of a physical quantity in terms of base dimensions, like \([M^aL^bT^c]\) for mass, length, and time powers.?
Velocity has dimensional formula \([LT^{-1}]\).?
Force has dimensional formula \([MLT^{-2}]\).?
In a physically meaningful equation, the dimensions of all terms on both sides must be the same.?
To check the dimensional consistency of equations, derive relations between quantities, and convert from one system of units to another.?
It cannot determine dimensionless constants (like 1/2, 2p), and it fails if quantities of different dimensions are added.?
Significant figures are the meaningful digits in a number that indicate the precision of a measurement, including all certain digits and the first doubtful digit.?
All non-zero digits are significant; zeros between non-zero digits are also significant.?
There are 3 significant figures: 2, 5, and the trailing zero after 5.?
Percentage error is \((absolute error/true or mean value)×100%\).?
Errors that occur in the same direction each time due to faulty instruments, wrong techniques, or personal bias; they cannot be reduced by repeating measurements alone.?
Errors that vary unpredictably from one measurement to another due to uncontrollable conditions; they can be reduced by taking many observations and averaging.?
The least count is the smallest value of a quantity that an instrument can measure accurately, equal to the value of one smallest division on its scale.?
It is the nearest power of 10 to the value of a quantity, giving a rough size estimate, e.g., \(3.2 × 10^7\) has order of magnitude 7.?
If Q=A±BQ=A±B, then ?Q˜?A+?B?Q˜?A+?B (absolute errors add).?
If Q=A×BQ=A×B or Q=A/BQ=A/B, then ?Q/Q˜?A/A+?B/B?Q/Q˜?A/A+?B/B (relative errors add).?
(\Delta Q / Q \approx
?V/V=3(?r/r)=3×(0.1/5)=0.06?V/V=3(?r/r)=3×(0.1/5)=0.06, so percentage error = 6%6%.?
Pressure = force/area, so \([P]=[MLT^{-2}]/[L^2]=[ML^{-1}T^{-2}]\).?
Work = force × distance, so \([W]=[MLT^{-2}][L]=[ML^2T{-2}]\).?
From \(F=Gm_1m_2/r^2\), \([G]=[M^{-1}L^3T^{-2}].?
From \(E=h\nu\), \([h]=[E]/[?]=[ML^2T^{-2}][T]=[ML^2T^{-1]}\).?
Impulse and momentum have the same dimensions: \([MLT-1]\).?
From \(P=sAT^4\), \([s]=[P]/[AT^4]=[MT^{-3}][L^{-2}K^{-4}]=[ML^{-2}T^{-3}K^{-4}]\).?
Assuming T?lagbT?lagb and equating dimensions gives T?l/g, independent of mass.?
Yes, each term has dimension \([LT-1]\), so it is dimensionally consistent.?
Dimensionally it matches energy, but physically the correct expression for kinetic energy is \(K=\frac{1}{2}mv^2\); dimensional analysis cannot detect the missing numerical factor.?
\(1\ N = 10^5\) dyne, since 1 kg = 1000 g and 1 m = 100 cm.?
\(1\ J = 10^7\) erg, because \(1\ N\ m = 10^5\ dyne × 10^2\) cm.?
\(1\ Å = 10^{-10}\) m, widely used for atomic-scale distances.?
There are 4 significant figures: 6, 9, and the two trailing zeros after 9.?
Precision refers to the closeness among repeated measurements; accuracy refers to closeness of a measurement to the true value.?
Repeated measurements reduce random errors and provide a better estimate of the true value through averaging.?
It builds strong fundamentals for dimensional analysis, unit conversion, error calculation, and checking equations—skills heavily used in JEE/NEET physics problems.
