Question

Match List - I with List - II.

List - I	List - II
A. Mass B. Damper C. Spring D. Force	I. Capacitor II. Voltage III. Resistor IV. Inductor

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

Hint:

Force-voltage analogy: \[ \text{Mass} \leftrightarrow \text{Inductor} \] \[ \text{Damper} \leftrightarrow \text{Resistor} \] \[ \text{Spring} \leftrightarrow \text{Capacitor} \] \[ \text{Force} \leftrightarrow \text{Voltage} \]

Answer 1

The Correct Option is D

Concept: Mechanical and electrical systems can be compared using analogies. In the force-voltage analogy:
• Mass corresponds to Inductor,
• Damper corresponds to Resistor,
• Spring corresponds to Capacitor,
• Force corresponds to Voltage. These analogies are important in control system modeling.

Step 1: Matching Mass. Mass stores kinetic energy and opposes changes in velocity. Similarly, an inductor stores magnetic energy and opposes changes in current. Therefore: \[ \text{Mass} \leftrightarrow \text{Inductor} \] Thus: \[ A \to IV \]

Step 2: Matching Damper. A damper dissipates mechanical energy through friction. A resistor dissipates electrical energy as heat. Therefore: \[ \text{Damper} \leftrightarrow \text{Resistor} \] Thus: \[ B \to III \]

Step 3: Matching Spring. A spring stores potential energy. Similarly, a capacitor stores electrical energy. Hence: \[ \text{Spring} \leftrightarrow \text{Capacitor} \] Thus: \[ C \to I \]

Step 4: Matching Force. In force-voltage analogy: \[ \text{Force} \leftrightarrow \text{Voltage} \] Hence: \[ D \to II \]

Step 5: Writing the final matching. Thus: \[ A-IV,\quad B-III,\quad C-I,\quad D-II \] Hence the correct option is: \[ \boxed{(4)} \]