Q. No.The equations of the displacement of two particles making SHM are represented by \(y_1 = a\sin(\omega t + \phi)\) and \(y_2 = a\cos(\omega t)\) respectively. The phase difference of the velocities of the two particles will be:
1. \(\frac{\pi}{2}+\phi\)
2. \(-\phi\)
3. \(\phi\)
4. \(\phi-\frac{\pi}{2}\)
| 1. | \( \frac{T}{12} \) | 2. | \(\frac{5 T}{12} \) |
| 3. | \( \frac{7 T}{12} \) | 4. | \(\frac{2 T}{3}\) |
The time period of a spring mass system at the surface of the earth is \(2~\text{s}.\) What will be the time period of this system on the moon where the acceleration due to gravity is \(\frac{1}{16}^\text{th}\) of the value of \(g\) on the earth's surface?
| 1. | \(\frac{1}{\sqrt{6}} ~\mathrm{s} \) | 2. | \(2 \sqrt{6}~ \mathrm{s} \) |
| 3. | \(2~ \mathrm{s} \) | 4. | \( 12~\mathrm{ s}\) |
| 1. | \(\pi \) | 2. | \(2 \pi \) |
| 3. | \(4 \pi \) | 4. | \(6 \pi\) |
A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration vector \(\vec a\) is correctly shown in:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
| 1. | \(2A,A\) | 2. | \(4A,0\) |
| 3. | \(A,A\) | 4. | \(0,2A\) |
| 1. | the motion is oscillatory but not SHM. |
| 2. | the motion is SHM with an amplitude \(a\sqrt{2}\). |
| 3. | the motion is SHM with an amplitude \(\sqrt{2}\). |
| 4. | the motion is SHM with an amplitude \(a\). |
1. \(\frac{\pi}{3}\)
2. \(\frac{2\pi}{3}\)
3. \(\frac{\pi}{6}\)
4. \(\frac{\pi}{2}\)
| 1. |  |
2. |  |
| 3. |  |
4. |  |
A block \(P\) of mass \(m\) is placed on a frictionless horizontal surface. Another block \(Q\) of same mass is kept on \(P\) and connected to the wall with the help of a spring of spring constant \(k\) as shown in the figure. \(\mu_s\) is the coefficient of friction between \(P\) and \(Q\). The blocks move together performing SHM of amplitude \(A\). The maximum value of the friction force between \(P\) and \(Q\) will be:
1. \(kA\)
2. \(\frac{kA}{2}\)
3. zero
4. \(\mu_s mg\)
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