Which of the units of the following physical quantities are derived? I. Area II. Thrust III. Pressure IV. Mass

To solve this, we need to distinguish between Base Quantities and Derived Quantities in Physics.

1. Analyze the Concepts

• Base Quantities: These are fundamental physical quantities that cannot be defined in terms of other physical quantities. There are seven base quantities in the SI system: Length, Mass, Time, Electric Current, Temperature, Luminous Intensity, and Amount of Substance.
• Derived Quantities: These are quantities that are expressed in terms of the base quantities through mathematical relationships (formulas).

2. Evaluate the Given Quantities

• I. Area: Area is calculated as $Length \times Length$ ($L^2$). Since it is derived from length, it is a derived quantity.
• II. Thrust: Thrust is a type of force. According to Newton's Second Law, $Force = mass \times acceleration$ ($M \times LT^{-2}$). Since it is derived from mass, length, and time, it is a derived quantity.
• III. Pressure: Pressure is defined as $Force / Area$. Since both Force and Area are derived, Pressure is also a derived quantity.
• IV. Mass: Mass is one of the seven fundamental SI base quantities. Therefore, it is not a derived quantity.

3. Conclusion

Based on the analysis:

• I (Area), II (Thrust), and III (Pressure) are derived.
• IV (Mass) is base.

Therefore, the quantities that are derived are I, II, and III only.

4. Exam Tip

A simple way to remember this is to look at the units. If the unit is a combination of base units (like $m^2$, $kg \cdot m/s^2$, or $N/m^2$), it is derived. If the unit is one of the standard seven (like $kg$, $m$, or $s$), it is a base quantity.