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Q. No.In simple harmonic motion, the ratio of acceleration of the particle to its displacement at any time is a measure of:
1.
Spring constant
2.
Angular frequency
3.
(Angular frequency)2
4.
Restoring force
Subtopic: Simple Harmonic Motion |
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Level 1: 80%+
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One end of a spring of force constant \(k\) is fixed to a vertical wall and the other to a block of mass \(m\) resting on a smooth horizontal surface. There is another wall at a distance \(x_0\) from the block. The spring is then compressed by \(2x_0\)
| 1. | \(\frac{1}{6} \pi \sqrt{ \frac{k}{m}}\) | 2. | \( \sqrt{\frac{k}{m}}\) |
| 3. | \(\frac{2\pi}{3} \sqrt{ \frac{m}{k}}\) | 4. | \(\frac{\pi}{4} \sqrt{ \frac{k}{m}}\) |
Subtopic: Spring mass system |
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Level 2: 60%+
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When the displacement is half the amplitude in an SHM, the ratio of potential energy to the total energy is:
1. \(\frac{1}{2}\)
2. \(\frac{1}{4}\)
3. \(1\)
4. \(\frac{1}{8}\)
1. \(\frac{1}{2}\)
2. \(\frac{1}{4}\)
3. \(1\)
4. \(\frac{1}{8}\)
Subtopic: Energy of SHM |
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Level 1: 80%+
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A block is connected to a relaxed spring and kept on a smooth floor. The block is given a velocity towards the right. Just after this:
| 1. | the speed of block starts decreasing but acceleration starts increasing. |
| 2. | the speed of the block as well as its acceleration starts decreasing. |
| 3. | the speed of the block starts increasing but its acceleration starts decreasing. |
| 4. | the speed of the block as well as acceleration start increasing. |
Subtopic: Spring mass system |
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Level 2: 60%+
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The amplitude and the time period in an SHM are \(0.5\) cm and \(0.4\) sec respectively. If the initial phase is \(\frac{\pi}{2}\) radian, then the equation of SHM will be:
1. \(y = 0.5\sin(5\pi t)\)
2. \(y = 0.5\sin(4\pi t)\)
3. \(y = 0.5\sin(2.5\pi t)\)
4. \(y = 0.5\cos(5\pi t)\)
1. \(y = 0.5\sin(5\pi t)\)
2. \(y = 0.5\sin(4\pi t)\)
3. \(y = 0.5\sin(2.5\pi t)\)
4. \(y = 0.5\cos(5\pi t)\)
Subtopic: Linear SHM |
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Level 2: 60%+
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A mass m is suspended from two springs of spring constant as shown in the figure below. The time period of vertical oscillations of the mass will be
1.
2.
3.
4.
Subtopic: Combination of Springs |
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Kinetic energy of a particle executing simple harmonic motion in straight line is \(pv^2\) and potential energy is \(qx^2,\) where \(v\) is speed at distance \(x\) from the mean position. The time period of the SHM is given by the expression:
1. \(2\pi \sqrt{\frac{q}{p}}\)
2. \(2\pi \sqrt{\frac{p}{q}}\)
3. \(2\pi \sqrt{\frac{q}{p+q}}\)
4. \(2\pi \sqrt{\frac{p}{p+q}}\)
1. \(2\pi \sqrt{\frac{q}{p}}\)
2. \(2\pi \sqrt{\frac{p}{q}}\)
3. \(2\pi \sqrt{\frac{q}{p+q}}\)
4. \(2\pi \sqrt{\frac{p}{p+q}}\)
Subtopic: Energy of SHM |
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Level 2: 60%+
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The potential energy of a particle oscillating along the \(x\text-\)axis is given as \(U = 20+(x-2)^2\) where \(U\) is in joules and \(x\) in metres. The total mechanical energy of the particle is \(36~\text{J}\). The maximum kinetic energy of the particle will be:
1. \(24~\text{J}\)
2. \(36~\text{J}\)
3. \(16~\text{J}\)
4. \(20~\text{J}\)
1. \(24~\text{J}\)
2. \(36~\text{J}\)
3. \(16~\text{J}\)
4. \(20~\text{J}\)
Subtopic: Energy of SHM |
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Level 2: 60%+
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