Question

Match List - I with List - II. 

Choose the correct answer from the options given below : 
 

• A. A-I, B-III, C-IV, D-II
• B. A-III, B-I, C-II, D-IV
• C. A-III, B-I, C-IV, D-II
• D. A-II, B-III, C-IV, D-I

Hint:

Dimensional analysis is a foolproof way to solve these matches. All the units in List II are ultimately equivalent to 1 Joule of energy ($1 \text{ J} = 1 \text{ Nm} = 1 \text{ Pa}\cdot\text{m}^3 = 1 \text{ VC} = 1 \text{ kg}\cdot\text{m}^2/\text{s}^2$). Mapping the specific formula variables quickly gives the answer.

Answer 1

The Correct Option is C

Step 1: Concept:
The question asks us to match different physical manifestations of work with their corresponding mathematical units based on their fundamental physics formulas.

Step 2: Key Formula or Approach:
Work has the fundamental SI unit of Joules (J). Different forms of work use different variables that multiply together to yield Joules:
- Mechanical Expansion: $W = \int P \, dV$
- Extension (Spring/Wire): $W = \int F \, dx$
- Gravitational (Raising weight): $W = mgh$
- Electrical: $W = VQ$

Step 3: Step-by-step Explanation:

• A. Expansion Work: The formula is Pressure $\times$ Change in Volume ($P\Delta V$).
Units: Pressure is measured in Pascals (Pa) and volume in cubic meters (m$^3$).
Unit combination: Pa m$^3$ (Matches III).

• B. Extension Work: Work done in stretching a wire or spring is Force $\times$ Extension distance ($F \cdot dx$).
Units: Force is Newtons (N) and distance is meters (m).
Unit combination: Nm (Matches I).

• C. Raising of weight: Gravitational potential energy work is mass $\times$ gravity $\times$ height ($mgh$).
Units: mass in Kg, gravity in m/s$^2$ (or ms$^{-2}$), and height in meters (m).
Unit combination: Kg ms$^{-2$m} (Matches IV).

• D. Electrical Work: The work done moving a charge across a potential difference is Voltage $\times$ Charge ($V \cdot Q$).
Units: Voltage in Volts (V) and Charge in Coulombs (C).
Unit combination: VC (Matches II).
The final matching sequence is A-III, B-I, C-IV, D-II.

Step 4: Final Answer:
The sequence that perfectly matches our derivation is option (C).