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Units and Measurements gives JEE Main one of its easiest marks, and students still lose it. Dimensional formulas, error propagation and the least count of an instrument are all short, mechanical and completely learnable. There is no concept to understand here that you do not already know — only a table to fix in memory and a rule for adding errors. Ten questions below. Give them ten honest minutes.
What this chapter carries in JEE Main
- Usually 1 to 2 questions every year, which is 4 to 8 marks.
- Dimensional formulas and pairs with the same dimensions are asked almost every year.
- Error propagation and instrument least count make up the rest.
What the syllabus says
In the syllabus (Unit 1, Units and Measurements): Units of measurement, system of units, SI units, fundamental and derived units, least count, significant figures, errors in measurement, dimensions of physical quantities, dimensional analysis and its applications.
Taken out in 2024: physics, technology and society; accuracy and precision of measuring instruments.
Taken from the NTA syllabus for JEE Main 2027. See the full syllabus, unit by unit.
Formulas you must know by heart
| Force, work, power | [MLT−2], [ML2T−2], [ML2T−3] |
| Planck constant | [ML2T−1] |
| Gravitational constant | [M−1L3T−2] |
| Viscosity and surface tension | [ML−1T−1] and [MT−2] |
| Electrical resistance | [ML2T−3A−2] |
| Error in a sum or difference | the absolute errors add |
| Error in a product or quotient | the percentage errors add |
| Error in apbq | p(Δa/a) + q(Δb/b) |
| Least count of a vernier | 1 main scale division − 1 vernier division |
| Least count of a screw gauge | pitch / number of circular scale divisions |
The error rule with powers is where most marks are lost. A quantity that is squared carries twice its own percentage error into the answer, and a cube carries three times. Check the powers before you add anything.
Ten questions. Give yourself ten minutes.
Write your answers down before you scroll. A question you looked up is a question you have not answered.
Q1. The dimensional formula of Planck’s constant is
- (a) [ML2T−1]
- (b) [ML2T−2]
- (c) [MLT−1]
- (d) [ML2T−3]
Q2. Which pair has the same dimensions?
- (a) work and power
- (b) work and torque
- (c) force and momentum
- (d) pressure and force
Q3. The dimensional formula of the coefficient of viscosity is
- (a) [ML−1T−1]
- (b) [MLT−1]
- (c) [ML−1T−2]
- (d) [MLT−2]
Q4. The number of significant figures in 0.00430 is
- (a) 2
- (b) 3
- (c) 5
- (d) 6
Q5. The percentage errors in measuring a and b are 2% and 3%. The percentage error in a2b is
- (a) 5%
- (b) 7%
- (c) 12%
- (d) 1%
Q6. The dimensional formula of the gravitational constant G is
- (a) [M−1L3T−2]
- (b) [ML3T−2]
- (c) [M−1L2T−2]
- (d) [ML−3T2]
Q7. A screw gauge of pitch 1 mm has 100 divisions on its circular scale. Its least count is
- (a) 0.1 mm
- (b) 0.01 mm
- (c) 0.001 mm
- (d) 1 mm
Q8. Which of these is dimensionless?
- (a) strain
- (b) stress
- (c) force constant
- (d) torque
Q9. The dimensional formula of electrical resistance is
- (a) [ML2T−3A−2]
- (b) [ML2T−3A−1]
- (c) [ML2T−2A−2]
- (d) [MLT−3A−2]
Q10. In an experiment L = 1.00 ± 0.01 m and T = 2.00 ± 0.02 s, and g is found from g = 4π2L/T2. The percentage error in g is
- (a) 1%
- (b) 2%
- (c) 3%
- (d) 5%
Answer key, with a hint for each
| Q1 | (a) | E = hν, so h = energy × time = [ML2T−2][T]. It also matches angular momentum. |
| Q2 | (b) | Both are force × distance, so both are [ML2T−2], even though one is a scalar and the other a vector. |
| Q3 | (a) | From F = ηA(dv/dx). The SI unit, the pascal second, carries the same thing. |
| Q4 | (b) | Leading zeros never count. The 4, the 3 and the trailing 0 do. |
| Q5 | (b) | 2 × 2% for a2, plus 3% for b. |
| Q6 | (a) | From F = Gm1m2/r2, rearranged for G. |
| Q7 | (b) | Least count = pitch / number of divisions = 1/100 mm. |
| Q8 | (a) | Strain is a length divided by a length. Refractive index and relative density are dimensionless too. |
| Q9 | (a) | From R = V/I, with V in [ML2T−3A−1]. |
| Q10 | (c) | 1% from L, and 2 × 1% from T2, giving 3% in all. |
Now mark yourself honestly
JEE Main marks the way it marks. Use the same rule here:
- +4 for a right answer
- −1 for a wrong one
- 0 for a blank
So ten questions here are out of 40. In the real paper, 25 Physics questions are out of 100.
If you scored 32 or more, the basics of this chapter are secure. Move to harder questions, not more of these.
If you scored below 24, do not feel bad about it. You have just found out something useful before the exam did. Go back to the formula table above, learn it properly, and sit these ten again tomorrow.
And if you guessed a few and they landed, count those as wrong. A guess that works once will not work in January.
The full chapter, on a clock
Ten questions tell you a little. Twenty-five tell you the truth.
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