Column $I$ describe 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 $II$ and indicate your answer by darkening appropriate bubbles in the $4 \times 4$ matrix given in the $ORS$.
| Column $I$ | Column $II$ |
| $(A)$ The object moves on the $\mathrm{x}$-axis under a conservative force in such a way that its "speed" and "position" satisfy $v=c_1 \sqrt{c_2-x^2}$, where $\mathrm{c}_1$ and $\mathrm{c}_2$ are positive constants. | $(p)$ The object executes a simple harmonic motion. |
| $(B)$ The object moves on the $\mathrm{x}$-axis in such a way that its velocity and its displacement from the origin satisfy $\mathrm{v}=-\mathrm{kx}$, where $\mathrm{k}$ is a positive constant. | $(q)$ The object does not change its direction. |
| $(C)$ The object is attached to one end of a massless spring of a given spring constant. The other end of the spring is attached to the ceiling of an elevator. Initially everything is at rest. The elevator starts going upwards with a constant acceleration a. The motion of the object is observed from the elevator during the period it maintains this acceleration. | $(r)$ The kinetic energy of the object keeps on decreasing. |
| $(D)$ The object is projected from the earth's surface vertically upwards with a speed $2 \sqrt{\mathrm{GM}_e / R_e}$, where, $M_e$ is the mass of the earth and $R_e$ is the radius of the earth. Neglect forces from objects other than the earth. | $(s)$ The object can change its direction only once. |
IIT 2007, Advanced
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