SI Units — Set 4

Correct Answer: A. Volt per meter

• **Volt per meter** = V/m (volts per metre) is the SI unit of electric field strength, representing the force per unit charge or the potential gradient. • **equivalent to N/C** — One V/m equals one newton per coulomb (N/C), since electric field strength E = F/q = V/d. • 💡 Wrong-option analysis: Coulomb per meter: not a unit of electric field strength; Ampere per meter: SI unit of magnetic field strength (H), not electric field; Volt-meter: not a recognised SI unit for electric field.

Correct Answer: D. Farad per meter

• **Farad per meter** = F/m is the SI unit of permittivity, measuring how much an electric field is reduced inside a dielectric medium. • **ε₀ = 8.854 × 10⁻¹² F/m** — The permittivity of free space (vacuum permittivity) is exactly 8.854 × 10⁻¹² F/m, a fundamental physical constant. • 💡 Wrong-option analysis: Ohm per meter: related to electrical resistivity (not permittivity); Henry per meter: SI unit of permeability (magnetic, not electric); Coulomb per meter: not a standard unit for permittivity.

Correct Answer: B. Henry per meter

• **Henry per meter** = H/m is the SI unit of magnetic permeability, measuring a material's ability to support the formation of a magnetic field. • **μ₀ = 4π × 10⁻⁷ H/m** — The permeability of free space (vacuum permeability) is 4π × 10⁻⁷ H/m, a key constant in electromagnetism. • 💡 Wrong-option analysis: Weber per meter: not the SI unit of permeability; Ampere per meter: SI unit of magnetic field strength (H-field), not permeability; Tesla per meter: not a standard SI unit for permeability.

Correct Answer: D. Watt per square meter

• **Watt per square meter** = W/m² is the SI unit of irradiance (radiant flux density), measuring power received per unit area of a surface. • **solar constant ~1,361 W/m²** — The solar irradiance at the top of Earth's atmosphere is about 1,361 W/m², used in solar energy calculations. • 💡 Wrong-option analysis: Watt per meter: not a unit of irradiance (missing the square); Joule per square meter: unit of radiant exposure (energy, not power flux); Lux: measures illuminance of visible light only, not total radiant power.

Correct Answer: A. Cubic meter per mole

• **Cubic meter per mole** = m³/mol is the SI unit of molar volume, representing the volume occupied by one mole of a substance. • **~0.0224 m³/mol** — At STP, one mole of an ideal gas occupies approximately 0.0224 m³ (22.4 litres), a key value in chemistry. • 💡 Wrong-option analysis: Mole per cubic meter: this is molar concentration (inverse), not molar volume; Liter per mole: a common practical unit but not the SI unit; Cubic meter: unit of volume, not molar volume (missing per mole).

Correct Answer: B. Radian per second

• **Radian per second** = rad/s is the SI unit of angular velocity, describing how fast an object rotates or revolves. • **ω = 2πf** — Angular velocity relates to frequency by ω = 2πf; a motor at 60 Hz has angular velocity 2π × 60 ≈ 377 rad/s. • 💡 Wrong-option analysis: Revolution per minute (RPM): common practical unit but not SI; Degree per second: not the SI unit (degrees are not SI for angles); Meter per second: unit of linear velocity, not angular velocity.

Correct Answer: C. Radian per second squared

• **Radian per second squared** = rad/s² is the SI unit of angular acceleration, measuring the rate of change of angular velocity. • **α = Δω/Δt** — Angular acceleration α = Δω/Δt; it is the rotational analogue of linear acceleration (m/s²). • 💡 Wrong-option analysis: Meter per second squared: unit of linear acceleration, not angular; Radian per second: unit of angular velocity (not acceleration); Degree per second squared: not the SI unit.

Correct Answer: D. Meter

• **Meter** = The metre (m) is the SI base unit of length, one of the seven fundamental SI units. • **speed of light** — Since 1983, the metre is defined by fixing the speed of light at exactly 299,792,458 m/s, making it independent of any physical artefact. • 💡 Wrong-option analysis: Centimeter: 1/100 of a metre, a derived sub-unit; Kilometer: 1,000 metres, a larger sub-unit; Millimeter: 1/1,000 of a metre, a sub-unit.

Correct Answer: C. Kilogram

• **Kilogram** = The kilogram (kg) is the SI base unit of mass and the only base unit whose name includes a prefix (kilo-). • **Planck constant** — Since 2019, the kilogram is defined by fixing Planck's constant at exactly 6.626 × 10⁻³⁴ J·s, replacing the physical prototype. • 💡 Wrong-option analysis: Quintal: 100 kg, a non-SI unit; Tonne: 1,000 kg (metric ton), a non-SI unit; Gram: 1/1,000 of a kilogram, a sub-unit.

Correct Answer: D. Second

• **Second** = The second (s) is the SI base unit of time, the foundation for all time-related measurements in science. • **caesium-133** — One second is defined as exactly 9,192,631,770 oscillations of the radiation from a caesium-133 atom, making atomic clocks the most accurate timekeepers. • 💡 Wrong-option analysis: Day: 86,400 seconds, a non-SI civil unit; Hour: 3,600 seconds, a non-SI unit; Minute: 60 seconds, a non-SI unit.