Question

Which of the following quantities have the same derived unit?

• A. Energy
• B. Pressure
• C. Work done
• D. Torque

Answer 1

Answer: (A), (C), (D)

The correct options are
A Energy
C Work done
D Torque

• Energy or work done have the same unit, as they both are given as the product of force and displacement, i.e. their unit is ${\text{kg m}}^2{\text{s}}^{-2}$ or commonly called joule ($\text{J}$).
• Torque or the moment of force is given as the product of force and the perpendicular distance, i.e. its unit is also ${\text{kg m}}^2{\text{s}}^{-2}$ or commonly called newton-metre ($\text{N.m}$).
• Pressure is defined as the force acting on unit area and thus has a unit of ${\text{kg m}}^{-1}{\text{s}}^{-2}$ or commonly called pascal ($\text{Pa}$).

Therefore, the quantities, moment of force or torque, energy and work done have basically the same unit, ${\text{kg m}}^2{\text{s}}^{-2}$, even though their commonly used units aren't the same.