Units and Measurement

Moment of inertia measures an object's resistance to rotational acceleration, calculated as I = Σmr². Mass is in kg and radius squared is in m², giving kg·m². m/s² is acceleration and N is force.

Capacitance measures a capacitor's ability to store charge per unit voltage (C = Q/V). The SI unit for capacitance is the farad (F), named after Michael Faraday. Ohm is the unit of resistance.

Torque measures rotational force and is calculated as τ = r × F (radius × force). Force is in Newtons (N) and radius in meters (m), giving the unit N·m. J/s is power (watt).

In nutrition, 'Calorie' (capital C) on food labels actually means kilocalorie (kcal), which equals 1,000 scientific calories (lowercase c). Both terms refer to the same energy measurement unit used for food, making 'Both A & B' correct.

Joule is the SI unit of energy, work, and heat. While option C lists 'Heat', the joule is more broadly a unit of all forms of energy including heat energy, mechanical work, and other energy forms. The question asks for the unit of joule, and heat is one form of energy measured in joules.

1 Joule = 10^7 ergs. The erg is the CGS unit of energy, while joule is the SI unit. The conversion is: 1 J = 1 kg × 1 m²/s² = 1000 g × 10000 cm²/s² = 10^7 g×cm²/s² = 10^7 ergs.

Ampere is the SI unit of electric current. Ohm measures resistance, watt measures power, and neither of these is the unit of current.

In the MKS (meter-kilogram-second) system, the unit of energy is the Joule. Volt is for potential difference, Ohm is for resistance, and Erg is the unit of energy in the CGS (centimeter-gram-second) system, not MKS.

Coulomb (C) is the standard unit for electric charge, measuring the quantity of electricity transported in one second by a current of one ampere. Volt measures potential difference, joule measures energy, and ampere measures current flow rate.

In the CGS (centimeter-gram-second) system, the base unit of length is the centimeter. The SI system uses meters as the base unit, but CGS was developed earlier and uses centimeter as its fundamental length unit.

Decibel (dB) is the standard unit used to measure the intensity or loudness of sound. It represents a logarithmic ratio of sound pressure or power. Dyne is a unit of force, Joule is a unit of energy, and Knot is a unit of speed used in navigation - none are related to sound measurement.

Conductance (G) is measured in siemens (S), historically called 'mho' (ohm spelled backward), and symbolized by an inverted omega (℧). All three representations - inverted omega, mho, and siemens - are valid ways to denote conductance units.