Final Matching and Correct Option

Using the standard force–voltage (impedance) analogy for translational mechanical systems, the correct matching is:

• P) Mass → 5) Inductance
• Q) Spring constant → 3) Reciprocal capacitance
• R) Displacement → 4) Charge
• S) Velocity → 1) Current

Correct option: (B) P-5, Q-3, R-4, S-1

Concept of Mechanical–Electrical Analogies

In the force–voltage (impedance) analogy, mechanical force corresponds to electrical voltage, and velocity corresponds to current, so power (force × velocity) maps to power (voltage × current).

With this analogy:

• Mass ↔ Inductance
• Damping ↔ Resistance
• Spring stiffness ↔ Reciprocal capacitance
• Displacement ↔ Charge

This creates a consistent mapping between mechanical and electrical domains.

Why P) Mass → 5) Inductance

In mechanics, Newton’s law for a mass m is F = m (dv/dt) — force is needed to change velocity.

In an electrical circuit, the inductor law is V = L (di/dt) — voltage is needed to change current.

Thus, inductance L plays the same inertial role as mass, resisting changes in current or motion. Therefore, mass ↔ inductance (P-5).

Why Q) Spring Constant → 3) Reciprocal Capacitance

For a mechanical spring, F = kx; the stiffer the spring (larger k), the more force required for a given displacement.

For a capacitor, Q = CV, which can be written as V = (1/C) Q; here 1/C acts like the stiffness against charge.

Since both have the same proportional relationship between stored quantity and applied potential, spring constant k ↔ reciprocal capacitance 1/C (Q-3).

Why R) Displacement → 4) Charge

Displacement x is the time integral of velocity: x = ∫v dt.

Charge q is the time integral of current: q = ∫i dt.

Since velocity corresponds to current, their integrated quantities must also correspond, so displacement ↔ charge (R-4).

Why S) Velocity → 1) Current

Velocity is the rate of change of displacement: v = dx/dt.

Current is the rate of change of charge: i = dq/dt.

Therefore, once displacement maps to charge, velocity ↔ current (S-1).

Why the Other Listed Matches Are Wrong

• Option (A): P-3, Q-5, R-4, S-1 → Incorrect because mass ↔ reciprocal capacitance and spring ↔ inductance are invalid.
• Option (C): P-3, Q-5, R-4, S-2 → Also incorrect since it mismatches both inertial and dynamic pairs, and incorrectly maps velocity to voltage.
• Option (D): P-5, Q-3, R-4, S-1 → Correct mapping according to the impedance analogy in control systems and analog modeling.

SEO-Focused Introduction for Exam Preparation

Mechanical and electrical system analogies are an essential concept in control systems and physics. They help convert complex mechanical models into equivalent electrical circuits that are easier to analyze.

By mastering how mechanical parameters like mass, spring constant, displacement, and velocity map to their electrical analogs—inductance, reciprocal capacitance, charge, and current—students can solve matching questions quickly and accurately in competitive exams such as GATE, CSIR NET, and university-level control systems courses.