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: Understanding the Concept:
This question tests the understanding of the analogies between physical quantities in translational (linear) motion and rotational motion. Each quantity in linear motion has a corresponding analogue in rotational motion.
Step 2: Detailed Explanation:
Let's find the rotational analogue for each quantity in List-I.

(A) Force (\(\vec{F}\)): In linear motion, force causes linear acceleration (\(\vec{F} = m\vec{a}\)). The rotational analogue is Torque (\(\vec{\tau}\)), which causes angular acceleration (\(\vec{\tau} = I\vec{\alpha}\)). Thus, (A) matches with (I).

(B) Distance covered (s): This is a linear displacement. The rotational analogue is angular displacement, or the Angle described (\(\theta\)). Thus, (B) matches with (II).

(C) Mass (m): Mass is the measure of inertia, i.e., resistance to change in linear motion. The rotational analogue is the Moment of inertia (I), which is the measure of resistance to change in rotational motion. Thus, (C) matches with (III).

(D) Linear velocity (\(\vec{v}\)): This is the rate of change of linear displacement. The rotational analogue is Angular velocity (\(\vec{\omega}\)), which is the rate of change of angular displacement. Thus, (D) matches with (IV).
Step 3: Final Answer:
The correct matching is (A)-(I), (B)-(II), (C)-(III), and (D)-(IV). This corresponds exactly to option (A).