Which of the following is a physical quantity? Which unit represents energy in SI? What is a derived unit?

a) A physical quantity is a property that can be measured and expressed numerically.

• Anger, Beauty, and Pain are subjective experiences or qualities, not directly measurable physical quantities.
• Temperature is a measurable physical quantity, typically expressed in units like Celsius, Fahrenheit, or Kelvin.

The correct option is Temperature.

b) The unit of energy in the SI system is the Joule (J).
The Joule can be expressed in terms of base units:

$$1 \text{ J} = 1 \text{ N} \cdot \text{m}$$

Since force ($F$) is mass ($m$) times acceleration ($a$), $F = ma$, the unit of force (Newton, N) is:

$$1 \text{ N} = 1 \text{ kg} \cdot \frac{\text{m}}{\text{s}^2}$$

Substituting this into the expression for Joule:

$$1 \text{ J} = \left(1 \text{ kg} \cdot \frac{\text{m}}{\text{s}^2}\right) \cdot \text{m} = 1 \text{ kg} \cdot \frac{\text{m}^2}{\text{s}^2}$$

Comparing this to the given options:

• $\text{kg} \cdot \text{m/s}^2$ is the unit of force (Newton).
• $\text{kg} \cdot \text{m}^2/\text{s}^2$ is the unit of energy (Joule).
• $\text{kg/m}^3$ is the unit of density.
• $\text{m/s}$ is the unit of speed or velocity.

The correct option is $\boxed{\text{kg} \cdot \text{m}^2/\text{s}^2}$.

c) Derived units are units that are formed by combining base units (like meter, kilogram, second). Base units are fundamental and independent.

• Newton (N): A unit of force, derived from $\text{kg} \cdot \text{m/s}^2$. It is a derived unit.
• Joule (J): A unit of energy, derived from $\text{kg} \cdot \text{m}^2/\text{s}^2$. It is a derived unit.
• Kilogram (kg): A unit of mass. It is one of the seven SI base units. Therefore, it is NOT a derived unit.

The correct option is Kilogram.