The correct option is A-3, B-4, C-2, D-1
Explanation
In the International System of Units (SI), derived quantities are expressed using combinations of base units or special named units. Understanding the physical definitions of these quantities helps in identifying their corresponding units.
- Force (D): Force is defined as the product of mass and acceleration ($F = m \times a$). Its SI unit is the Newton ($N$). Therefore, D matches 1.
- Power (B): Power is the rate at which work is done or energy is transferred ($P = \text{Work} / \text{Time}$). Its SI unit is the Watt ($W$), which is equivalent to one Joule per second. Therefore, B matches 4.
- Work (A): Work is mechanically defined as the product of force and displacement in the direction of the force ($W = F \cdot d$). Consequently, its unit can be expressed as Newton-metre ($N\ m$). Therefore, A matches 3.
- Energy (C): Energy is defined as the capacity to do work. The standard SI unit for all forms of energy is the Joule ($J$). Therefore, C matches 2.
While Work and Energy are dimensionally equivalent and both can be measured in Joules (where $1 \ J = 1 \ N\ m$), in this specific matching context, Work is paired with its definitional components ($N\ m$) and Energy with its standard named unit ($J$).
Key Takeaway:
Work and Energy share the same dimensions ($ML^2T^{-2}$) and the unit Joule. However, Work is explicitly the product of Force and Distance ($N\ m$), whereas Power is the time rate of energy consumption ($J/s$ or Watt).