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Match List-I with List-II.

List-I (Graphs) (a) Displacement-time graph with decreasing amplitude (Damped) (b) Displacement-time graph with constant amplitude (Undamped) (c) Force-displacement graph (Linear relationship, F = -kx) (d) Energy-time graph (Constant total energy)

List-II (Situations) (i) Total mechanical energy is conserved (ii) Bob of a pendulum is oscillating under negligible air friction (iii) Restoring force of a spring (iv) Bob of a pendulum is oscillating along with air friction

Choose the correct answer from the options given below:

A

(a)-(iv), (b)-(ii), (c)-(iii), (d)-(i)

B

(a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)

C

(a)-(i), (b)-(iv), (c)-(iii), (d)-(ii)

D

(a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)

Step-by-Step Solution

  1. Damped Oscillation (a): When a pendulum oscillates with air friction (damping force), energy is dissipated, and the amplitude decreases with time. This matches with (iv) Bob of a pendulum is oscillating along with air friction .
  2. Undamped Oscillation (b): In the absence of friction (negligible air resistance), the amplitude of oscillation remains constant (Ideal SHM). This matches with (ii) Bob of a pendulum is oscillating under negligible air friction.
  3. Restoring Force (c): For a spring, the restoring force obeys Hooke's Law (F=kxF = -kx), which implies a linear relationship between Force and Displacement with a negative slope. This matches with (iii) Restoring force of a spring .
  4. Conservation of Energy (d): In an ideal SHM system (conservative forces only), the total mechanical energy (Kinetic + Potential) remains constant over time. This is represented by a straight horizontal line in an energy-time graph. This matches with (i) Total mechanical energy is conserved.
  5. Conclusion: The correct matching sequence is (a)-(iv), (b)-(ii), (c)-(iii), (d)-(i).
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