Units, Dimensions & Error Analysis
Practice JEE Main Units, Dimensions & Error Analysis chapter-wise PYQs online. Vernier calipers, screw gauge, dimensional formulas & step-by-step solutions.
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🎯 High-Yield Syllabus Breakdown
These high-frequency concepts account for over 90% of all questions asked in Units, Dimensions & Error Analysis:
- Dimensional Analysis & Principle of Homogeneity
- Percentage Error & Propagation in Products/Powers (ΔZ/Z = a·ΔA/A + b·ΔB/B)
- Vernier Callipers: Least Count = 1 MSD - 1 VSD
- Screw Gauge & Spherometer Zero Error Corrections
- Significant Figures & Rounding Rules
⚡ Essential Formulas & Speed Shortcuts
Formulas and time-saving shortcuts to solve Units & Dimensions questions in under 45 seconds:
Power Rule for Errors: If Z = Aᵃ Bᵇ / Cᶜ, then (ΔZ/Z)_max = a(ΔA/A) + b(ΔB/B) + c(ΔC/C).
Common Dimensional Equivalences: Work = Energy = Torque = [M L² T⁻²].
Resistance = [M L² T⁻³ A⁻²], Capacitance = [M⁻¹ L⁻² T⁴ A²].
📖 Sample Solved Exam Questions
Preview authentic questions from this chapter with full step-by-step solutions:
💡 View Step-by-Step Solution & Answer
Correct Answer: 8%
- Step 1: The formula for kinetic energy is KE = ½ m v².
- Step 2: Take fractional error: (ΔKE / KE)_max = (Δm / m) + 2(Δv / v).
- Step 3: Multiply by 100 to get percentage error: %ΔKE = %Δm + 2(%Δv).
- Step 4: Substitute given errors: %ΔKE = 2% + 2(3%) = 2% + 6% = 8%.
⚡ Speed Tip: Power Rule in Errors: Powers become multiplying factors: ΔKE/KE = Δm/m + 2(Δv/v) = 2 + 2(3) = 8%.
💡 View Step-by-Step Solution & Answer
Correct Answer: Angular momentum
- Step 1: Energy of a photon is E = hν ⇒ h = E / ν = (Energy) / (Frequency).
- Step 2: Dimensions of Energy are [M L² T⁻²] and Frequency is [T⁻¹].
- Step 3: Therefore, [h] = [M L² T⁻²] / [T⁻¹] = [M L² T⁻¹].
- Step 4: Angular momentum L = mvr has dimensions [M] · [L T⁻¹] · [L] = [M L² T⁻¹]. Thus, [h] = [L].
⚡ Speed Tip: Bohr Postulate: Angular momentum L = n h / (2π). Thus h and L always share identical dimensions [M L² T⁻¹].
💡 View Step-by-Step Solution & Answer
Correct Answer: 0.01 mm
- Step 1: Formula for the least count of a screw gauge: Least Count = (Pitch) / (Number of circular scale divisions).
- Step 2: Given Pitch = 0.5 mm.
- Step 3: Number of divisions = 50.
- Step 4: Least Count = 0.5 mm / 50 = 0.01 mm.
⚡ Speed Tip: Least Count Formula: LC = Pitch / N = 0.5 / 50 = 0.01 mm.
❓ Frequently Asked Questions (FAQs)
How to calculate Vernier Calipers Least Count?
Least Count = 1 Main Scale Division (MSD) - 1 Vernier Scale Division (VSD) = (1 - n/m) MSD.