Jee Advanced
Waves
IIT-JEE 2007 Paper 2 Offline
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.
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| Column I | Column II | ||
|---|---|---|---|
| (A) | The object moves on the 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 \(c_1\) and \(c_2\) are positive constants. | (P) | The object executes a simple harmonic motion. |
| (B) | The object moves on the x-axis in such a way that its velocity and its displacement from the origin satisfy \(v=-kx\), where \(k\) 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 \(2\sqrt {GMe/{\mathop{\rm Re}\nolimits} }\), 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. |