📝 Practice Section
Easy (CBSE) → Moderate (NEET/JEE Main) → Advanced (JEE Advanced) · Answer Key Included
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Level Note
These questions test definition + basic application. Every question here must become automatic. If you hesitate here, revisit the Core Concepts page.
Q1 — DefinitionsEasy
Define a physical quantity. Give two examples that are fundamentally different.
A physical quantity is one that can be measured and expressed as a numerical value × unit. Examples: Length (5 m) — fundamental; Velocity (30 m/s) — derived.
Q2 — SI UnitsEasy
Name all 7 SI base quantities with their units and symbols.
1. Length — metre (m)
2. Mass — kilogram (kg)
3. Time — second (s)
4. Electric current — ampere (A)
5. Temperature — kelvin (K)
6. Amount of substance — mole (mol)
7. Luminous intensity — candela (cd)
2. Mass — kilogram (kg)
3. Time — second (s)
4. Electric current — ampere (A)
5. Temperature — kelvin (K)
6. Amount of substance — mole (mol)
7. Luminous intensity — candela (cd)
Q3 — DimensionsEasy
Write dimensional formulas for: (a) velocity (b) force (c) work/energy
(a) Velocity = [LT⁻¹]
(b) Force = [MLT⁻²]
(c) Work = [ML²T⁻²]
(b) Force = [MLT⁻²]
(c) Work = [ML²T⁻²]
Q4 — DimensionlessEasy
Why is strain dimensionless? Explain with the definition.
Strain = ΔL/L = change in length / original length. Both are lengths [L]. So [Strain] = [L]/[L] = [M⁰L⁰T⁰] — dimensionless. It is a pure ratio.
Q5 — Least CountEasy
Find the least count of a screw gauge with pitch = 1 mm and 100 circular scale divisions.
LC = Pitch / Number of divisions = 1 mm / 100 = 0.01 mm
Q6 — Significant FiguresEasy
Round off 12.376 to 3 significant figures.
12.376 → 3 sig figs → 12.4 (the 4th sig fig is 7 > 5, so round up the 3)
Q7 — Error TypesEasy
Distinguish between systematic and random error with one example of each.
Systematic: Consistent in one direction. Example: clock running slow → all time readings are lower. Cannot be reduced by repetition.
Random: Unpredictable fluctuations. Example: slight variations in stopwatch readings by a human. Reduced by taking the mean of many readings.
Random: Unpredictable fluctuations. Example: slight variations in stopwatch readings by a human. Reduced by taking the mean of many readings.
Q8 — Addition RuleEasy
Add 2.34 + 5.1 + 0.222 with correct significant figures.
Sum = 7.662. Least decimal places among addends = 1 (from 5.1). Answer = 7.7 (rounded to 1 decimal place)
Level Note
These questions appear frequently in NEET and JEE Main. Pattern recognition and formula application without confusion. 1–2 minutes per question target.
Q1 — Dimensions of ConstantsModerate
Find dimensional formulas of: (a) surface tension (b) viscosity (c) Planck's constant h
(a) ST = F/l = [MLT⁻²]/[L] = [MT⁻²]
(b) η = stress/(velocity gradient) = [ML⁻¹T⁻²]/[T⁻¹] = [ML⁻¹T⁻¹]
(c) h = E/f = [ML²T⁻²]/[T⁻¹] = [ML²T⁻¹]
(b) η = stress/(velocity gradient) = [ML⁻¹T⁻²]/[T⁻¹] = [ML⁻¹T⁻¹]
(c) h = E/f = [ML²T⁻²]/[T⁻¹] = [ML²T⁻¹]
Q2 — Dimensional DerivationModerate
If T ∝ lᵃgᵇ for a pendulum, find a and b using dimensional analysis.
T = kl^a g^b
[T] = [L]^a [LT⁻²]^b = [L^(a+b) T^(−2b)]
Compare T: −2b = 1 → b = −½
Compare L: a+b = 0 → a = ½
So T ∝ √(l/g)
[T] = [L]^a [LT⁻²]^b = [L^(a+b) T^(−2b)]
Compare T: −2b = 1 → b = −½
Compare L: a+b = 0 → a = ½
So T ∝ √(l/g)
Q3 — % ErrorModerate
For R = V/I where ΔV/V = 2% and ΔI/I = 3%, find the percentage error in R.
ΔR/R = ΔV/V + ΔI/I = 2% + 3% = 5%
Q4 — Dimensional CheckModerate
Check dimensional correctness of: v² = u² + 2as
[v²] = [L²T⁻²]
[u²] = [L²T⁻²] ✓
[2as] = [LT⁻²][L] = [L²T⁻²] ✓
All terms have same dimension → Dimensionally correct.
[u²] = [L²T⁻²] ✓
[2as] = [LT⁻²][L] = [L²T⁻²] ✓
All terms have same dimension → Dimensionally correct.
Q5 — Vernier LCModerate
In a Vernier calipers, 10 VSD = 9 MSD and 1 MSD = 1 mm. Find the least count.
1 VSD = (9/10) MSD = 0.9 mm
LC = 1 MSD − 1 VSD = 1 − 0.9 = 0.1 mm
LC = 1 MSD − 1 VSD = 1 − 0.9 = 0.1 mm
Q6 — Multiplication Sig FigsModerate
Calculate 3.2 × 1.456 and express with correct significant figures.
3.2 × 1.456 = 4.6592
3.2 has 2 sig figs, 1.456 has 4 sig figs → Answer has 2 sig figs
4.6592 → 4.7
3.2 has 2 sig figs, 1.456 has 4 sig figs → Answer has 2 sig figs
4.6592 → 4.7
Level Note
These require combining multiple concepts. JEE Advanced style: high thinking, low routine algebra. Spend 3–5 minutes per problem.
Q1 — Multi-Constant DimensionalJEE Advanced
If Y ∝ Gᵃhᵇcᶜ where G is gravitational constant, h is Planck's constant, and c is speed of light, find a, b, c such that Y has dimensions of Length.
[G] = [M⁻¹L³T⁻²], [h] = [ML²T⁻¹], [c] = [LT⁻¹]
Write: [L] = [M⁻ᵃ⁺ᵇ · L^(3a+2b+c) · T^(−2a−b−c)]
M: −a+b=0 → b=a
L: 3a+2b+c=1
T: −2a−b−c=0 → c=−3a
Substituting: 3a+2a−3a=1 → 2a=1 → a=½
b=½, c=−3/2
Y ∝ √(Gh/c³) — This is the Planck length!
Write: [L] = [M⁻ᵃ⁺ᵇ · L^(3a+2b+c) · T^(−2a−b−c)]
M: −a+b=0 → b=a
L: 3a+2b+c=1
T: −2a−b−c=0 → c=−3a
Substituting: 3a+2a−3a=1 → 2a=1 → a=½
b=½, c=−3/2
Y ∝ √(Gh/c³) — This is the Planck length!
Q2 — Non-Standard Base UnitsJEE Advanced
If Force (F), Velocity (V), and Time (T) are taken as fundamental quantities, express the dimensions of: (a) mass (b) energy (c) momentum
[L] = [VT] (from V = L/T)
[M] = [F·T/V] = [FTV⁻¹]
(a) Mass = [FTV⁻¹]
(b) Energy = F × L = F × VT = [FVT]
(c) Momentum = m×v = [FTV⁻¹][V] = [FT]
[M] = [F·T/V] = [FTV⁻¹]
(a) Mass = [FTV⁻¹]
(b) Energy = F × L = F × VT = [FVT]
(c) Momentum = m×v = [FTV⁻¹][V] = [FT]
Q3 — Error in Compound FormulaJEE Advanced
For density ρ = 3M/(4πr³), find % error if M is measured with 2% error and r with 1.5% error.
Δρ/ρ = ΔM/M + 3·Δr/r
= 2% + 3 × 1.5%
= 2% + 4.5%
= 6.5%
Note: π and 3 are exact (no error). r has power 3 → its error is tripled.
= 2% + 3 × 1.5%
= 2% + 4.5%
= 6.5%
Note: π and 3 are exact (no error). r has power 3 → its error is tripled.
Q4 — Dimension Matching TrapJEE Advanced
Which of these pairs has the SAME dimensional formula? (a) Torque and Energy (b) Impulse and Momentum (c) Pressure and Stress (d) All of these
(a) Torque = r × F = [ML²T⁻²]; Energy = [ML²T⁻²] → SAME ✓
(b) Impulse = F·t = [MLT⁻¹]; Momentum = mv = [MLT⁻¹] → SAME ✓
(c) Pressure = F/A = [ML⁻¹T⁻²]; Stress = F/A = [ML⁻¹T⁻²] → SAME ✓
Answer: (d) All of these. This is a very common JEE matching question.
(b) Impulse = F·t = [MLT⁻¹]; Momentum = mv = [MLT⁻¹] → SAME ✓
(c) Pressure = F/A = [ML⁻¹T⁻²]; Stress = F/A = [ML⁻¹T⁻²] → SAME ✓
Answer: (d) All of these. This is a very common JEE matching question.
Q5 — Screw Gauge with Zero ErrorJEE Advanced
Screw gauge: pitch = 0.5 mm, 50 divisions, MSR = 3 mm, CSR = 35, positive zero error = 0.02 mm. Find corrected diameter.
LC = 0.5/50 = 0.01 mm
Observed reading = 3 + 35 × 0.01 = 3 + 0.35 = 3.35 mm
Positive zero error = +0.02 mm (instrument reads 0.02 more than true)
Corrected = Observed − Zero Error = 3.35 − 0.02 = 3.33 mm
Observed reading = 3 + 35 × 0.01 = 3 + 0.35 = 3.35 mm
Positive zero error = +0.02 mm (instrument reads 0.02 more than true)
Corrected = Observed − Zero Error = 3.35 − 0.02 = 3.33 mm
How to Use This
Check only after attempting. For wrong answers, note the concept, go back to that page, and re-attempt after 24 hours. Do NOT just read the answer key — work backwards from what you got wrong.
Easy Level — Quick Reference
| Q# | Key Answer / Formula | Core Concept |
|---|---|---|
| E1 | Physical quantity = value × unit | Definition |
| E2 | m, kg, s, A, K, mol, cd | SI base units |
| E3 | [LT⁻¹], [MLT⁻²], [ML²T⁻²] | Dimensional formulas |
| E4 | ΔL/L is ratio → dimensionless | Dimensionless quantities |
| E5 | LC = 0.01 mm | Screw gauge |
| E6 | 12.4 | Rounding rules |
| E7 | Systematic = biased; Random = fluctuating | Error types |
| E8 | 7.7 | Addition sig figs |
Moderate Level
| Q# | Key Answer | Core Concept |
|---|---|---|
| M1 | [MT⁻²], [ML⁻¹T⁻¹], [ML²T⁻¹] | Dimensional formulas of constants |
| M2 | a = ½, b = −½ | Power matching |
| M3 | 5% | Fractional error — division |
| M4 | Dimensionally correct | Homogeneity principle |
| M5 | 0.1 mm | Vernier LC |
| M6 | 4.7 | Multiplication sig figs |
Advanced Level
| Q# | Key Answer | Core Concept |
|---|---|---|
| A1 | a=½, b=½, c=−3/2 → Planck length | Multi-constant dimension |
| A2 | [FTV⁻¹], [FVT], [FT] | Non-standard base units |
| A3 | 6.5% | Power rule in error |
| A4 | (d) All pairs match | Same-dimension pairs |
| A5 | 3.33 mm | Zero error correction |
🏔 Challenge Problems
Challenge 1
Construct a quantity with dimensions of Velocity using only G (gravitational constant) and ρ (density). Find the combination.
Challenge 2
A student measures l = 20.0 ± 0.1 cm and T = 0.90 ± 0.01 s for a pendulum. Calculate g and its % error. Is the accepted value of 9.8 m/s² within the error range?
Challenge 3
Show that [ε₀μ₀] = [L⁻²T²]. Hence, what does 1/√(ε₀μ₀) represent dimensionally?