Question

Match the physical quantities in List I with the corresponding SI units in List II:

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

Hint:

Express common energy units like Joules (J) as Newton-meters (N m) to simplify matching questions with non-standard SI base derivatives.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks to match the physical quantities given in List-I with their appropriate SI units expressed in basic force-based combinations in List-II.

Step 2: Key Concept and Approach:
We will find the formula and derived SI unit for each quantity:
- Torque ($\tau$) = Force $\times$ distance.
- Stress ($\sigma$) = Force / Area.
- Latent heat ($L$) = Heat Energy / Mass.
- Power ($P$) = Work Done / Time.

Step 3: Detailed Explanation:

• A. Torque: Torque ($\tau = \vec{r} \times \vec{F}$) has the SI unit of Newton-meter (N m).
Thus, A matches with III.

• B. Stress: Stress is restoring force per unit area.
Its unit is $\text{N/m}^2$, which is written as $\text{N m}^{-2}$.
Thus, B matches with IV.

• C. Latent heat: Latent heat ($L = \frac{Q}{m}$) is heat energy per unit mass.
Its unit is Joules per kilogram ($\text{J kg}^{-1}$).
Since $1\text{ Joule} = 1\text{ N m}$, the unit becomes $\text{N m kg}^{-1}$.
Thus, C matches with II.

• D. Power: Power ($P = \frac{W}{t}$) is energy expended per unit time.
Its unit is Joules per second ($\text{J s}^{-1}$).
Substituting $1\text{ J} = 1\text{ N m}$ gives $\text{N m s}^{-1}$.
Thus, D matches with I.


Step 4: Final Answer:
The correct matching sequence is A-III, B-IV, C-II, D-I, corresponding to Option (B).