Column $I$ describes some situations in which a small object moves. Column $II$ describes some characteristics of these motions. Match the situation in Column $I$ with the characteristics in Column $II$.
Column $I$Column $II$
$(A)$ The object moves on the $x$-axis under a conservative force such that its speed $v = c_1 \sqrt{c_2 - x^2}$,where $c_1, c_2 > 0$.$(p)$ The object executes simple harmonic motion.
$(B)$ The object moves on the $x$-axis such that its velocity $v = -kx$,where $k > 0$.$(q)$ The object does not change its direction.
$(C)$ An object is attached to a spring in an elevator accelerating upwards with constant acceleration $a$. The motion is observed from the elevator.$(r)$ The kinetic energy of the object keeps on decreasing.
$(D)$ The object is projected vertically upwards with speed $2 \sqrt{GM_e / R_e}$.$(s)$ The object can change its direction only once.

  • A
    $A \rightarrow (p), B \rightarrow (q) \& (r), C \rightarrow (p), D \rightarrow (r) \& (q)$
  • B
    $A \rightarrow (r), B \rightarrow (q) \& (r), C \rightarrow (p), D \rightarrow (p) \& (q)$
  • C
    $A \rightarrow (q), B \rightarrow (r) \& (r), C \rightarrow (p), D \rightarrow (q) \& (r)$
  • D
    $A \rightarrow (s), B \rightarrow (q) \& (s), C \rightarrow (p), D \rightarrow (s) \& (r)$

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Match $List-I$ with $List-II$:
| | $List-I$ ($x-y$ graphs) | | $List-II$ (Situations) |
|---|---|---|---|
| $(a)$ | Damped oscillation graph | $(i)$ | Total mechanical energy is conserved |
| $(b)$ | Linear graph $y = -kx$ | $(ii)$ | Bob of a pendulum is oscillating under negligible air friction |
| $(c)$ | Simple harmonic motion graph | $(iii)$ | Restoring force of a spring |
| $(d)$ | Energy conservation graph ($K$.$E$. and $P$.$E$. curves) | $(iv)$ | Bob of a pendulum is oscillating along with air friction |
Choose the correct answer from the options given below:

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