Question

Match List-I with List-II

\[ \begin{array}{|l|l|} \hline \textbf{List-I} & \textbf{List-II} \\ \hline (A) \; \text{Force} & (I) \; \text{Torque} \\ (B) \; \text{Distance covered} & (II) \; \text{Angle described} \\ (C) \; \text{Mass} & (III) \; \text{Moment of inertia} \\ (D) \; \text{Linear velocity} & (IV) \; \text{Angular velocity} \\ \hline \end{array} \]
Choose the correct answer from the options given below:

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

Hint:

Creating a simple two-column table of linear and rotational analogues can be very helpful for studying this topic.
Position (x) \(\leftrightarrow\) Angle (\(\theta\))
Velocity (v) \(\leftrightarrow\) Angular Velocity (\(\omega\))
Acceleration (a) \(\leftrightarrow\) Angular Acceleration (\(\alpha\))
Mass (m) \(\leftrightarrow\) Moment of Inertia (I)
Force (F) \(\leftrightarrow\) Torque (\(\tau\))
Momentum (p=mv) \(\leftrightarrow\) Angular Momentum (L=I\(\omega\))

Answer 1

The Correct Option is A

Step 1: Conceptual Foundation:
This problem assesses understanding of the analogies between physical quantities governing translational (linear) and rotational motion. Each linear motion quantity possesses a corresponding rotational analogue.
Step 2: Detailed Analysis:
We will identify the rotational counterpart for each quantity listed in List-I.

(A) Force (\(\vec{F}\)): In linear motion, force induces linear acceleration (\(\vec{F} = m\vec{a}\)). The rotational equivalent is Torque (\(\vec{\tau}\)), which induces angular acceleration (\(\vec{\tau} = I\vec{\alpha}\)). Therefore, (A) corresponds to (I).

(B) Distance Covered (s): This represents linear displacement. The rotational analogue is angular displacement, also known as the Angle Described (\(\theta\)). Consequently, (B) corresponds to (II).

(C) Mass (m): Mass quantifies inertia, signifying resistance to changes in linear motion. The rotational equivalent is the Moment of Inertia (I), which measures resistance to changes in rotational motion. Thus, (C) corresponds to (III).

(D) Linear Velocity (\(\vec{v}\)): This is defined as the rate of change of linear displacement. The rotational analogue is Angular Velocity (\(\vec{\omega}\)), which represents the rate of change of angular displacement. Hence, (D) corresponds to (IV).
Step 3: Conclusion:
The accurate pairings are (A)-(I), (B)-(II), (C)-(III), and (D)-(IV). This exact configuration matches option (A).