SI Units — Set 3

Correct Answer: A. Steradian

• **Steradian** = The steradian (sr) is the SI unit for measuring solid angles in three-dimensional space, the 3D equivalent of the radian. • **4π sr** — A complete sphere subtends a solid angle of exactly 4π steradians (≈12.566 sr) at its centre. • 💡 Wrong-option analysis: Arcsecond: a subdivision of degree for plane angles, not a solid angle unit; Degree: unit for plane angles only; Radian: SI unit for plane (2D) angles, not solid (3D) angles.

Correct Answer: B. Siemens

• **Siemens** = The siemens (S) is the SI unit of electrical conductance and admittance, representing the ease with which current flows. • **1 A/V (reciprocal ohm)** — One siemens equals one ampere per volt; conductance is the reciprocal of resistance (S = 1/Ω). • 💡 Wrong-option analysis: Henry: SI unit of inductance; Farad: SI unit of capacitance; Ohm: SI unit of resistance (conductance is its inverse).

Correct Answer: C. Dioptre

• **Dioptre** = The dioptre (D) is the unit for optical power of a lens or curved mirror, equal to the reciprocal of the focal length in metres. • **1/focal length** — A lens with focal length 0.5 m has power 2 D; convex (converging) lenses have positive dioptres, concave (diverging) lenses negative. • 💡 Wrong-option analysis: Meter: unit of length, not optical power; Lux: unit of illuminance; Lumen: unit of luminous flux.

Correct Answer: A. Pascal-second

• **Pascal-second** = The pascal-second (Pa·s) is the SI unit of dynamic viscosity, describing a fluid's internal resistance to flow. • **10 poise** — One pascal-second equals 10 poise (CGS unit); water has a dynamic viscosity of about 0.001 Pa·s at 20°C. • 💡 Wrong-option analysis: Poise: CGS unit of dynamic viscosity (not SI); Stoke: CGS unit of kinematic viscosity (not SI); Newton-meter: unit of torque or energy.

Correct Answer: A. Joule per mole-kelvin

• **Joule per mole-kelvin** = J/(mol·K) is the SI unit of molar entropy, measuring the degree of disorder per mole of substance per degree of temperature. • **thermodynamics** — Molar entropy combines the joule (energy), mole (substance amount), and kelvin (temperature) — three key thermodynamic quantities. • 💡 Wrong-option analysis: Newton per meter: unit of surface tension or spring constant; Watt per meter-kelvin: unit of thermal conductivity; Joule per kelvin: unit of entropy (not molar entropy, which requires per mole).

Correct Answer: C. Ampere per meter

• **Ampere per meter** = Ampere per metre (A/m) is the SI unit of magnetic field strength (H-field), distinct from magnetic flux density. • **H-field vs B-field** — Magnetic field strength H (A/m) is related to free currents, while magnetic flux density B (tesla) includes the effect of the medium. • 💡 Wrong-option analysis: Tesla: SI unit of magnetic flux density (B-field), not field strength (H-field); Henry: SI unit of inductance; Weber: SI unit of magnetic flux.

Correct Answer: B. Joule per kilogram-kelvin

• **Joule per kilogram-kelvin** = J/(kg·K) is the SI unit of specific heat capacity, representing the energy needed to raise 1 kg of a substance by 1 K. • **4,186 J/(kg·K)** — Water has one of the highest specific heat capacities at 4,186 J/(kg·K), which is why it is used as a coolant. • 💡 Wrong-option analysis: Joule per kilogram: unit of specific energy (not specific heat); Watt per kelvin: unit of thermal conductance; Joule per kelvin: unit of heat capacity (not specific, i.e., not per unit mass).

Correct Answer: B. Watt per meter-kelvin

• **Watt per meter-kelvin** = W/(m·K) is the SI unit of thermal conductivity, measuring a material's ability to conduct heat. • **copper ~400 W/(m·K)** — Copper has a thermal conductivity of about 400 W/(m·K), while air is only ~0.025 W/(m·K), explaining why metals feel cold to touch. • 💡 Wrong-option analysis: Newton per meter: unit of surface tension; Pascal-second: unit of dynamic viscosity; Joule per kelvin: unit of heat capacity (not conductivity).

Correct Answer: C. Newton-meter

• **Newton-meter** = The newton-metre (N·m) is the SI unit of torque (rotational force), representing the moment of force about an axis. • **same dimensions as joule** — Although N·m has the same dimensions as joule (energy), torque is not energy and the unit is written as N·m, not joule. • 💡 Wrong-option analysis: Pascal-meter: not a standard SI torque unit; Watt-second: equals joule (energy), not torque; Joule-meter: not a recognised SI unit.

Correct Answer: B. Newton per meter

• **Newton per meter** = N/m is the SI unit of surface tension, measuring the force acting per unit length along the surface of a liquid. • **water ~0.072 N/m** — Water's surface tension is about 0.072 N/m at 20°C, which is why small insects can walk on water. • 💡 Wrong-option analysis: Newton per meter squared: this is the pascal (pressure), not surface tension; Pascal-meter: not a standard surface tension unit; Joule per meter: equivalent to N/m but less commonly used for surface tension.