⚡ Quick Revision
One-page summary · Key formulas · Memory tricks · 30-second challenge · Flashcards
⚡ Night Before Exam — Units & Measurements
Everything you need. Nothing extra. Read once. Recall everything.
Physical Quantities
- Quantity = Numerical value × Unit
- 7 fundamental (base) quantities in SI
- All others are derived
- Units change with system; Dimensions don't
7 SI Base Quantities
- Length → m
- Mass → kg
- Time → s
- Current → A
- Temperature → K
- Amount → mol
- Luminous intensity → cd
Dimensional Analysis — Uses
- ✓ Check equation correctness
- ✓ Derive relationships
- ✓ Convert units
- ✗ Cannot find dimensionless constants
- ✗ Cannot confirm physical completeness
Error Summary
- Systematic → consistent bias, not reduced by repetition
- Random → fluctuating, reduced by averaging
- |ΔA+ΔB| always for sum/difference
- Relative errors add for product/quotient
- Power multiplies relative error
Significant Figures
- Non-zero digits → always significant
- Leading zeros → never significant
- Trailing zeros in decimal → significant
- Addition/subtraction → least decimal places
- Multiplication/division → least sig figs
Instruments
- Vernier LC = 1 MSD − 1 VSD
- Screw Gauge LC = Pitch / Divisions
- Reading = MSR + (CSR × LC)
- Corrected = Observed − Zero Error
- Positive ZE → subtract; Negative ZE → add
Must-Know Dimensional Formulas
[F] = MLT⁻²
[W/E] = ML²T⁻²
[P_power] = ML²T⁻³
[P_pressure] = ML⁻¹T⁻²
[ρ] = ML⁻³
[η] = ML⁻¹T⁻¹
[ST] = MT⁻²
[h] = ML²T⁻¹
[G] = M⁻¹L³T⁻²
[μ₀] = MLT⁻²A⁻²
[ε₀] = M⁻¹L⁻³T⁴A²
[B] = MT⁻²A⁻¹
[R_elec] = ML²T⁻³A⁻²
[L_ind] = ML²T⁻²A⁻²
[C_cap] = M⁻¹L⁻²T⁴A²
[k_B] = ML²T⁻²K⁻¹
Error Propagation
Z = A ± B → ΔZ = ΔA + ΔB
Absolute errors add — always
Z = AB/C → ΔZ/Z = ΔA/A + ΔB/B + ΔC/C
Relative errors add
Z = Aⁿ → ΔZ/Z = |n| × ΔA/A
Power multiplies relative error
g = 4π²l/T² → Δg/g = Δl/l + 2ΔT/T
Classic exam example
Dimension Memory Hooks
Force
"Force = Mass pushes Acceleration" → M × LT⁻²
[MLT⁻²]
Energy/Work
"Force × Distance = add one L to force" → MLT⁻² × L
[ML²T⁻²]
Pressure
"Force spread over Area = subtract L² from force numerator" → MLT⁻²/L²
[ML⁻¹T⁻²]
Viscosity (η)
"Pressure × Time" → ML⁻¹T⁻² × T
[ML⁻¹T⁻¹]
Planck's h
"h = E/f = Energy / Frequency = ML²T⁻²/T⁻¹" = Energy × Time
[ML²T⁻¹]
G (Gravitational)
"G comes from F=Gm₁m₂/r² → G = Fr²/m² = MLT⁻² × L² / M² "
[M⁻¹L³T⁻²]
Same Dimensions Pairs
Torque = Work [ML²T⁻²] | Impulse = Momentum [MLT⁻¹] | Stress = Pressure [ML⁻¹T⁻²] | h = Angular Momentum [ML²T⁻¹]
⚡ All common JEE traps
Trap 1: Addition/subtraction → sig figs rule. Wrong! Use decimal place rule for addition.
Trap 2: Errors subtract in subtraction. Wrong! Absolute errors always add regardless of the operation.
Trap 3: Dimensionally correct = physically correct. Wrong! Correct → valid form, not complete physics.
Trap 4: Repeated readings fix systematic errors. Wrong! They reduce random error only.
Trap 5: Newton is a fundamental unit. Wrong! N = kg m s⁻² → it is derived.
Trap 6: Dimensionless = unitless. Not always. Angle (radians), strain, refractive index are dimensionless but have conventional units or context.
Trap 7: Dimensional analysis can derive all constants. Wrong! Cannot get 2, π, ½, 6π from dimensions alone.
Trap 8: 2.3 and 2.300 are identical in measurement. Wrong! 2.300 signals 4 sig figs; 2.3 signals 2 sig figs.
Trap 9: Mass and weight are the same quantity. Wrong! Mass = [M], scalar. Weight = [MLT⁻²], vector force.
Trap 10: In non-standard base unit problems, use memorized dimensions directly. Wrong! Re-derive [M] and [L] first, then substitute.
Click each card to flip and reveal the answer.
Dimension of Viscosity η?
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[ML⁻¹T⁻¹]
Dimension of Planck's constant h?
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[ML²T⁻¹]
Same as Angular Momentum
Same as Angular Momentum
Vernier Calipers Least Count Formula?
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LC = 1 MSD − 1 VSD
Dimension of Gravitational Constant G?
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[M⁻¹L³T⁻²]
Error rule for Z = Aⁿ?
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ΔZ/Z = |n| × ΔA/A
Which has dimension [ML²T⁻²]?
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Work, Energy, Torque — all same!
Dimension of Permittivity ε₀?
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[M⁻¹L⁻³T⁴A²]
Addition of measurements: 52.01 + 153.2?
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205.2
1 decimal place (from 153.2)
1 decimal place (from 153.2)
Click any card to flip · Click again to reset
⏱ 30-Second Revision Challenge
Answer all 5 from memory in 30 seconds. If you can't, you need one more pass through the concept.
1
Write the 7 SI base units (symbols only).
2
Write dimensions of Force, Pressure, Energy, Viscosity.
3
State one use AND one limitation of dimensional analysis.
4
State one key difference between systematic and random error.
5
What rule applies to significant figures in addition? In multiplication?
Model Answers — 30 Second Challenge
1. m, kg, s, A, K, mol, cd
2. Force [MLT⁻²] | Pressure [ML⁻¹T⁻²] | Energy [ML²T⁻²] | Viscosity [ML⁻¹T⁻¹]
3. Use: Check equation correctness. Limitation: Cannot determine dimensionless constants (2, π, ½).
4. Systematic = consistent bias (not reduced by repetition). Random = fluctuates (reduced by averaging).
5. Addition → least decimal places. Multiplication → least significant figures.