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 \(A~\text{to}~B\)) - 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 |
© 2024 GoodEd Technologies Pvt. Ltd.