Question

Match List - I with List - II 

Choose the most appropriate answer from the option given below : 
 

• A. (a)-(i), (b)-(iii), (c)-(iv), (d)-(ii)
• B. (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
• C. (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)
• D. (a)-(iii), (b)-(i), (c)-(iv), (d)-(ii)

Hint:

Remember that Energy, Work, and Torque all share the same dimensions: \(ML^2T^{-2}\).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
To match the lists, we need to find the dimensional formula for each physical quantity based on its fundamental definition.
Step 2: Detailed Explanation:
1. Torque (\( \tau \)): Defined as Force \(\times\) perpendicular distance.
\[ [\tau] = [MLT^{-2}] \times [L] = [ML^2T^{-2}] \]
Matches with (iii).
2. Impulse (\( J \)): Defined as Force \(\times\) time.
\[ [J] = [MLT^{-2}] \times [T] = [MLT^{-1}] \]
Matches with (i).
3. Tension (\( T \)): It is a type of Force.
\[ [T] = [MLT^{-2}] \]
Matches with (iv).
4. Surface Tension (\( S \)): Defined as Force per unit length.
\[ [S] = \frac{[MLT^{-2}]}{[L]} = [MT^{-2}] \]
Matches with (ii).
Mapping: (a)-(iii), (b)-(i), (c)-(iv), (d)-(ii).
Step 3: Final Answer:
The correct matching is (a)-(iii), (b)-(i), (c)-(iv), (d)-(ii).