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Part of ME-01 — Units, Measurements & Errors

Exam Cheat Sheet

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7 SI Base Units

m · kg · s · A · K · mol · cd

Critical Dimensional Formulas

QuantityFormula
Velocity[M^{0}$$L^{1}$$T^{-1}]
Acceleration[M^{0}$$L^{1}$$T^{-2}]
Force / Torque[M^{1}$$L^{1}$$T^{-2}]
Energy / Work / Torque[M^{1}$$L^{2}$$T^{-2}]
Power[M^{1}$$L^{2}$$T^{-3}]
Pressure / Stress / Young's / Energy density[M^{1}$$L^{-1}$$T^{-2}]
Momentum[M^{1}$$L^{1}$$T^{-1}]
Angular momentum[M^{1}$$L^{2}$$T^{-1}]
Surface tension[M^{1}$$L^{0}$$T^{-2}]
Viscosity[M^{1}$$L^{-1}$$T^{-1}]

Error Rules (3 lines)

  • Z = A ± B → ΔZ\Delta Z = ΔA\Delta A + ΔB\Delta B
  • Z = AB or A/B → ΔZ\Delta Z/Z = ΔA\Delta A/A + ΔB\Delta B/B
  • Z = Aⁿ → ΔZ\Delta Z/Z = n·ΔA\Delta A/A

Sig Figs (2 rules)

  • Leading zeros: NEVER count them
  • Trailing zeros after decimal: ALWAYS count them

Unit Conversion Formula

n2=n1(M1M2)a(L1L2)b(T1T2)cn_2 = n_1 \left(\frac{M_1}{M_2}\right)^a \left(\frac{L_1}{L_2}\right)^b \left(\frac{T_1}{T_2}\right)^c

G Conversion: SI → CGS

G=6.67×10−11 N m2 kg−2=6.67×10−8 dyne cm2 g−2G = 6.67 \times 10^{-11} \text{ N m}^2 \text{ kg}^{-2} = 6.67 \times 10^{-8} \text{ dyne cm}^2 \text{ g}^{-2}

Limitations of Dimensional Analysis

  1. Cannot find dimensionless constants (e.g., 1/2, 2π)
  2. Cannot distinguish formulas sharing same dimensions

NEET Traps

  • Error in division: ADD relative errors (never subtract)
  • 0.0046 → 2 sig figs (not 4)
  • Dimensional correctness ≠ physical correctness
  • Systematic errors persist even after averaging

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