Q. No.A particle moves in a circular path with a continuously increasing speed. Its motion is:
1. periodic
2. oscillatory
3. simple harmonic
4. none of them
| 1. | \(e^{-\omega t}\) | 2. | \(\text{sin}\omega t\) |
| 3. | \(\text{sin}\omega t+\text{cos}\omega t\) | 4. | \(\text{sin}(\omega t+\pi/4)\) |
Trains travel between station A and station B: on the way up (from A to B) - they travel at a speed of \(80\) km/h, while on the return trip the trains travel at twice that speed. The services are maintained round the clock. Trains leave station A every \(30\) min for station B and reach B in \(2\) hrs. All trains operate continuously, without any rest at A or B.
| 1. | the frequency of trains leaving B must be twice as much as A. |
| 2. | the frequency of trains leaving B must be half as much as A. |
| 3. | the frequency of trains leaving B is equal to that at A |
| 4. | the situation is impossible to maintain unless larger number of trains are provided at A. |
1. \(5\) cm/s
2. \(10\) cm/s
3. at least \(10\) cm/s
4. at most \(10\) cm/s
\(x=A+A\text{sin}\omega t\\ y=A-A\text{sin}\omega t\)
are superposed on a particle, along \(x\) and \(y\) directions. The resultant of these motions is:
| 1. | circular motion |
| 2. | SHM along \(x\)-axis |
| 3. | SHM along \(y\)-axis |
| 4. | SHM, but along a direction other than \(x\) or \(y\)-axis |
| Statement I: | A graph of its acceleration vs displacement (from mean position) is a straight line. |
| Statement II: | A graph of its velocity vs displacement (from mean position) is an ellipse. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
The maximum speed and acceleration of a particle undergoing SHM are \(v_0\) and \(a_0,\) respectively. The time period of the SHM is:
1. \(\frac{2\pi v_0}{a_0}\)
2. \(\frac{2\pi a_0}{v_0}\)
3. \(\frac{v_0}{a_0}\)
4. \(\frac{2v_0}{a_0}\)
| 1. | \(0.01~\text{Hz}\) | 2. | \(0.02~\text{Hz}\) |
| 3. | \(0.03~\text{Hz}\) | 4. | \(0.04~\text{Hz}\) |
The time period of a particle in simple harmonic motion is equal to the time between consecutive appearances of the particle at a particular point in its motion. This point is:
| 1. | the mean position |
| 2. | an extreme position |
| 3. | between the mean position and the positive extreme |
| 4. | between the mean position and the negative extreme |
| 1. | uniform circular motion |
| 2. | elliptical motion |
| 3. | linear SHM |
| 4. | angular SHM along a circle |
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