Units and Measurements for JEE Main
Units and Measurements is a short chapter, but its rules support calculations throughout JEE Main Physics. The questions may look simple; the challenge is applying dimensions, powers and rounding rules without careless mistakes.
For efficient preparation, separate the chapter into three skills: deriving dimensions from a known relation, handling errors in a calculated quantity and reporting a measured value with correct precision. Then test those skills using mixed MCQs.
Important Topics to Revise
These areas cover the reasoning patterns commonly used in Units and Measurements practice.
SI Units
Know base quantities, base units and commonly used derived units.
Dimensions
Derive formulae for force, pressure, energy, momentum, power and constants.
Dimensional Analysis
Check a relation and use the powers of dimensions during conversion.
Significant Figures
Apply zero rules, rounding and decimal-place rules correctly.
Measurement Errors
Use absolute, relative and percentage error definitions accurately.
Propagation of Errors
Combine errors for products, quotients and quantities raised to powers.
Units and Measurements Formula Revision
Use this list as a recall check, not just a reading list.
How to Solve These Questions Systematically
Write the physical relation
If the required quantity is familiar, start from its defining equation instead of trying to memorise every dimensional formula independently.
Replace terms with base dimensions
Use mass, length, time and any other relevant base quantity. Collect exponents carefully at the end.
Identify the operation in error questions
For addition and subtraction use absolute errors; for multiplication and division use fractional or percentage errors; use powers as multipliers.
Check the reported precision
For addition/subtraction, use the least number of decimal places. For multiplication/division, use the least number of significant figures.
JEE Main Units and Measurements Important Questions
Attempt the question first, then open the detailed answer.
The dimensions of impulse are the same as those of:
Show answer and explanation
Answer: B. Impulse is force multiplied by time. Its dimensions are \([M L T^{-2}][T]=[M L T^{-1}]\), which are the dimensions of momentum.
The number of significant figures in 0.005060 is:
Show answer and explanation
Answer: C. Leading zeros are not significant. The digits 5, 0, 6 and the final zero are significant, so the number has four significant figures.
If \(R=A/B\), and percentage errors in \(A\) and \(B\) are 3% and 2%, respectively, the maximum percentage error in \(R\) is:
Show answer and explanation
Answer: B. For division, maximum percentage errors add. Thus, the error in \(R\) is \(3\%+2\%=5\%\).
Which expression is dimensionally consistent for displacement \(s\), velocity \(u\), acceleration \(a\) and time \(t\)?
Show answer and explanation
Answer: A. \(ut\) has dimensions of length, and \(at^2\) also has dimensions of length. Numerical constants do not affect dimensional consistency.
If 1 m equals \(10^2\) cm, then 1 m\(^2\) equals:
Show answer and explanation
Answer: C. Square the conversion: \(1\,m^2=(10^2\,cm)^2=10^4\,cm^2\).
A quantity \(Q\) is proportional to \(x^3\). If percentage error in \(x\) is 1.5%, the maximum percentage error in \(Q\) is:
Show answer and explanation
Answer: C. Since \(Q\propto x^3\), maximum percentage error in \(Q\) is \(3\times1.5\%=4.5\%\).
The SI unit of pressure is:
Show answer and explanation
Answer: C. Pressure is measured in pascal, where \(1\,Pa=1\,N/m^2\).
A smaller least count of a measuring instrument generally indicates:
Show answer and explanation
Answer: B. A smaller least count permits smaller divisions to be read and generally improves precision. It does not guarantee that all measurement errors are zero.
Continue Your JEE Main Physics Practice
After solving these questions, attempt a timed chapter test. Review both incorrect and guessed answers so that dimensions and error rules become automatic in mixed numerical problems.
Try the Free Mock TestCommon Mistakes to Avoid
- Counting leading zeros as significant figures.
- Forgetting to square or cube a unit conversion for area or volume.
- Using percentage-error rules for addition or subtraction.
- Ignoring the exponent of a variable in an error-propagation question.
- Assuming a dimensionally correct equation is automatically physically complete.
- Checking solutions before making an independent attempt.
JEE Main Units and Measurements FAQs
Which topics are important in Units and Measurements for JEE Main?
SI units, dimensions, dimensional analysis, significant figures, least count, unit conversion and error propagation are key revision areas.
How should I practise this chapter for JEE Main?
Revise one rule at a time, solve questions without viewing answers, record the reason for every mistake and reattempt incorrect questions after a short revision gap.
Can dimensional analysis determine every Physics formula?
No. It can check dimensional consistency and help find forms of some relations, but it cannot determine dimensionless constants or establish a complete physical law.
Are these official JEE Main previous-year questions?
No. These are original JEE Main-style practice questions prepared for revision. Refer to official sources for exact previous-year papers.