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 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. |
A massless rod is suspended by two identical strings AB and CD of equal length. A block of mass $m$ is suspended from point $O$ such that BO is equal to $x$. Further, it is observed that the frequency of 1st harmonic (fundamental frequency) in AB is equal to 2 nd harmonic frequency in CD. Then, length of BO is
Two waves $y_1=\mathrm{A} \cos (0.5 \pi x-100 \pi t)$ and $y_2=\mathrm{A} \cos (0.467 \pi x-92 \pi t)$ are travelling in a pipe placed along $x$-axis.
Find the number of times the intensity is maximum in the time interval of 1 sec.
Two waves $y_1=\mathrm{A} \cos (0.5 \pi x-100 \pi t)$ and $y_2=\mathrm{A} \cos (0.467 \pi x-92 \pi t)$ are travelling in a pipe placed along $x$-axis.
Find the wave velocity of louder sound.
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