SI Units — Set 5

Correct Answer: D. Square meter

• **Square meter** = The square metre (m²) is the SI derived unit of area, defined as the area of a square with sides of one metre. • **derived unit** — It is derived directly from the SI base unit metre; 1 m² = 10,000 cm² and 1 hectare = 10,000 m². • 💡 Wrong-option analysis: Square kilometer: a larger area unit (1 km² = 10⁶ m²), not the SI base; Acre: a non-SI imperial/customary unit; Hectare: a practical unit (10,000 m²) but not the SI unit.

Correct Answer: D. Cubic meter

• **Cubic meter** = The cubic metre (m³) is the SI derived unit of volume, representing the space occupied by a cube with sides of one metre. • **1,000 litres** — One cubic metre equals exactly 1,000 litres (1 L = 0.001 m³), though litre is not a formal SI unit. • 💡 Wrong-option analysis: Gallon: non-SI unit used in the USA and UK; Liter: commonly used but not the formal SI unit for volume; Milliliter: 0.001 litres, a sub-unit of litre.

Correct Answer: A. Meter per second

• **Meter per second** = Metres per second (m/s) is the SI derived unit for both speed and velocity. • **velocity is a vector** — Velocity includes direction while speed does not; the SI unit m/s applies to both, and the speed of light is approximately 3 × 10⁸ m/s. • 💡 Wrong-option analysis: Kilometer per hour: commonly used but not the SI unit (1 km/h = 0.278 m/s); Mile per hour: non-SI imperial unit; Knot: nautical unit (1 knot = 0.514 m/s).

Correct Answer: A. Meter per second squared

• **Meter per second squared** = m/s² is the SI unit of acceleration, measuring the rate of change of velocity per unit time. • **g ≈ 9.8 m/s²** — Earth's gravitational acceleration is approximately 9.8 m/s², meaning a freely falling object gains 9.8 m/s of speed every second. • 💡 Wrong-option analysis: Newton per meter: unit of spring constant (stiffness), not acceleration; Meter per second: unit of velocity, not acceleration; Kilometer per hour squared: non-SI unit.

Correct Answer: D. Kilogram per cubic meter

• **Kilogram per cubic meter** = kg/m³ is the SI unit of density, representing mass per unit volume. • **water = 1,000 kg/m³** — Pure water has a density of 1,000 kg/m³ at 4°C; iron is about 7,874 kg/m³ and air is about 1.2 kg/m³. • 💡 Wrong-option analysis: Kilogram per liter: equivalent numerically to g/cm³, but liter is not the SI unit for volume; Pound per cubic foot: non-SI imperial unit; Gram per cubic centimeter: CGS unit (numerically same as kg/L, but not SI).

Correct Answer: C. Kilogram-meter per second

• **Kilogram-meter per second** = kg·m/s is the SI unit of linear momentum, defined as the product of mass and velocity (p = mv). • **conservation law** — Momentum is conserved in all closed systems; it is equivalent to newton-second (N·s) since 1 N = 1 kg·m/s². • 💡 Wrong-option analysis: Joule-second: unit of action (Planck's constant has this unit), not momentum; Newton-meter: unit of torque or energy; Watt-meter: not a standard physics unit.

Correct Answer: C. Newton-second

• **Newton-second** = N·s is the SI unit of impulse, representing the change in momentum caused by a force acting over time. • **J = F × Δt** — Impulse equals force multiplied by time (J = F·Δt); since 1 N = 1 kg·m/s², one newton-second equals one kg·m/s (same as momentum). • 💡 Wrong-option analysis: Pascal-second: SI unit of dynamic viscosity, not impulse; Joule-second: unit of action, not impulse; Watt-second: equals joule (energy), not impulse.

Correct Answer: A. 10^6

• **10^6** = The prefix 'mega' (symbol M) represents one million (10⁶), used for large quantities such as megawatt and megahertz. • **uppercase M** — 'Mega' is represented by uppercase M to distinguish it from 'milli' (lowercase m = 10⁻³); 1 MW = 10⁶ W. • 💡 Wrong-option analysis: 10^9: this is 'giga' (G); 10^12: this is 'tera' (T); 10^3: this is 'kilo' (k).

Correct Answer: B. 10^-9

• **10^-9** = The prefix 'nano' (symbol n) represents one-billionth (10⁻⁹), used for extremely small scales such as nanometer and nanosecond. • **nanotechnology** — A nanometre (10⁻⁹ m) is about 10 times the diameter of a hydrogen atom; the prefix is central to nanotechnology. • 💡 Wrong-option analysis: 10^-6: this is 'micro' (μ); 10^-12: this is 'pico' (p); 10^-15: this is 'femto' (f).

Correct Answer: A. Seven

• **Seven** = There are exactly seven SI base units: metre (length), kilogram (mass), second (time), ampere (current), kelvin (temperature), mole (substance), and candela (luminous intensity). • **all others derived** — Every other SI unit is derived from combinations of these seven; for example, the newton = kg·m/s² combines kilogram, metre, and second. • 💡 Wrong-option analysis: Five: incorrect count (missing ampere and candela); Nine: incorrect (exceeds the actual number); Eleven: incorrect.