PA01 — Units, Dimensions & Basic Physics

Newton (N) is the SI unit of force. 1 N = 1 kg·m/s². Named after Isaac Newton. Joule = unit of energy/work; Pascal = unit of pressure; Watt = unit of power.

Energy (work) has dimensions [ML²T⁻²]. Force = [MLT⁻²]; Pressure = [ML⁻¹T⁻²]; Power = [ML²T⁻³]. This is a key dimensional formula tested regularly in AFCAT.

Pressure = Force/Area = [MLT⁻²]/[L²] = [ML⁻¹T⁻²]. Stress has the same dimensions as pressure. Velocity = [LT⁻¹]; Energy = [ML²T⁻²]; Momentum = [MLT⁻¹].

A light year is the distance light travels in one year ≈ 9.46 × 10¹⁵ metres. It is a unit of distance, not time. Light travels at 3 × 10⁸ m/s. Used to measure astronomical distances between stars and galaxies.

In 0.00507, the leading zeros are not significant — they are placeholders. The significant figures are 5, 0, and 7 = 3 significant figures. The zero between 5 and 7 IS significant (captive zero). Rules: leading zeros = not significant; captive zeros = significant; trailing zeros after decimal = significant.

Strain = change in length / original length = [L/L] = dimensionless. Refractive index, specific gravity, angle (in radians), and coefficient of friction are also dimensionless. Dimensionless quantities have no units.

Coulomb (C) is the SI unit of electric charge. 1 C = 1 A·s (ampere × second). Ampere = unit of current; Volt = unit of potential difference; Farad = unit of capacitance. 1 electron carries charge 1.6 × 10⁻¹⁹ C.

Dynamic viscosity has the SI unit Pa·s (pascal-second), also written as N·s/m². It measures a fluid's resistance to flow. Water: ~0.001 Pa·s; Honey: ~10 Pa·s. Surface tension = N/m; Pressure = Pa; Power = W.

The principle of homogeneity: in any valid physical equation, the dimensions on the left-hand side must equal the dimensions on the right-hand side. This principle is used to check equations, derive relations, and convert units. It cannot determine dimensionless constants.

1 parsec ≈ 3.26 light years ≈ 3.086 × 10¹⁶ m. It is the distance at which 1 AU subtends an angle of 1 arcsecond. Used to measure stellar distances. 1 light year ≈ 9.46 × 10¹⁵ m (option D is the definition of a light year, not a parsec).

E = hν → h = E/ν = [ML²T⁻²]/[T⁻¹] = [ML²T⁻¹]. Planck's constant h = 6.626 × 10⁻³⁴ J·s. It has dimensions of angular momentum (action). This formula appears in quantum mechanics: E = hν, de Broglie: λ = h/p.

Pressure = Force/Area = [ML⁻¹T⁻²]; Stress = Force/Area = [ML⁻¹T⁻²]. Both have identical dimensions. Work ≠ Power ([ML²T⁻²] vs [ML²T⁻³]); Force ≠ Momentum ([MLT⁻²] vs [MLT⁻¹]); Energy ≠ Power ([ML²T⁻²] vs [ML²T⁻³]).

1 kWh = 1000 W × 3600 s = 3,600,000 J = 3.6 × 10⁶ J. The kWh is the unit used by electricity companies to measure household energy consumption. 1 unit of electricity = 1 kWh. AFCAT tests this conversion frequently.

Candela (cd) is the SI base unit of luminous intensity. It measures the power of light in a specific direction per unit solid angle. Lumen = unit of luminous flux; Lux = unit of illuminance (lumen per m²). Candela is one of the 7 SI base units.

9.865 rounded to 3 significant figures: the 4th significant figure is 5. By the round-half-up rule: round the 6 up to 7. Result = 9.87. The three significant figures are 9, 8, and 7. Significant figure rounding is important in reporting experimental results.

From F = Gm₁m₂/r²: G = Fr²/(m₁m₂) = [MLT⁻²][L²]/[M²] = [M⁻¹L³T⁻²]. G = 6.674 × 10⁻¹¹ N·m²/kg². The negative power of M indicates G decreases with increasing mass — unusual among fundamental constants.

Newton is a derived SI unit (kg·m/s²), not a fundamental unit. The 7 SI base units are: metre (length), kilogram (mass), second (time), ampere (current), kelvin (temperature), mole (amount), candela (luminous intensity). All other units are derived from these.

Accuracy: how close a measurement is to the true/accepted value. Precision: how close repeated measurements are to each other. A measurement can be precise but inaccurate (systematic error) or accurate but imprecise (random errors). AFCAT distinguishes these clearly.

Angular velocity (ω) = angle/time = radian/second (rad/s). It measures the rate of rotation. Hertz (Hz) = cycles per second = s⁻¹ (for frequency). Radian is the unit of angle (dimensionless). Linear velocity = m/s; angular velocity = rad/s.

Checking homogeneity: v = [LT⁻¹]; u = [LT⁻¹]; at = [LT⁻²][T] = [LT⁻¹]. All three terms have dimensions [LT⁻¹] (velocity). The equation is dimensionally consistent. Dimensional analysis verifies equation correctness but cannot determine dimensionless constants like ½ in s = ut + ½at².