Q. No.| (a) | periodic motion. |
| (b) | simple harmonic motion. |
| (c) | periodic but not simple harmonic motion. |
| (d) | non-periodic motion. |
Choose the correct option from the given ones:
| 1. | (a) and (c) only |
| 2. | (a), (b) and (c) only |
| 3. | (b) and (d) only |
| 4. | (d) only |
Which of the following statements accurately describe various types of motion?
| 1. | A motion that repeats itself at fixed intervals of time is known as periodic motion. |
| 2. | A to-and-fro movement of a particle along the same path about a mean position is called oscillatory motion. |
| 3. | An oscillatory motion that can be expressed mathematically using a single sine or cosine function is termed simple harmonic motion. |
| 4. | All of the above. |
| Assertion (A): | The angular velocity of the moon revolving about the earth is more than the angular velocity of the earth revolving around the sun. |
| Reason (R): | The time taken by the moon to revolve around the earth is less than the time taken by the earth to revolve around the sun. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
| 1. | \(\dfrac{\pi}{\omega}\) | 2. | \(\dfrac{2\pi}{\omega}\) |
| 3. | \(\dfrac{1}{\omega}\) | 4. | \(\dfrac{\omega}{2\pi}\) |
A particle moves in a circular path with a uniform speed. Its motion is:
| 1. | periodic |
| 2. | oscillatory |
| 3. | simple harmonic |
| 4. | angular simple harmonic |
The figure depicts four \(({x\text-t})\) plots for the linear motion of a particle.
| (a) |  |
| (b) |  |
| (c) |  |
| (d) |  |
Which of the following is true?
| 1. | (a) is periodic but (c) is not periodic |
| 2. | (b) is periodic but (d) is not periodic. |
| 3. | (b) and (d) are periodic. |
| 4. | only (c) is periodic. |
1. \(2 \pi \sqrt{\frac{l}{g} } \)
2. \(2 \pi \sqrt{\frac{g}{l}} \)
3 \(\frac{1}{2} \pi \sqrt{\frac{l}{g}}\)
4. \(\frac{1}{2 \pi} \sqrt{\frac{g}{l}}\)
Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance (\(R/2\)) from the earth's center, where '\(R\)' is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period :
1. \(\frac{2 \pi R}{g} \)
2. \(\frac{\mathrm{g}}{2 \pi \mathrm{R}} \)
3. \(\frac{1}{2 \pi} \sqrt{\frac{g}{R}} \)
4. \(2 \pi \sqrt{\frac{R}{g}} \)
1. \(\sqrt{3}\text{ m}\)
2. \(2\sqrt{3}\text { m}\)
3. \(\frac{\sqrt{3}}{2} \text{ m}\)
4. \(\frac{1}{\sqrt{2}}\text{ m}\)
When two displacements are represented by \(y_1 = a \text{sin}(\omega t)\) and \(y_2 = b\text{cos}(\omega t)\) are superimposed, then the motion is:
| 1. | not simple harmonic. |
| 2. | simple harmonic with amplitude \(\dfrac{a}{b}\). |
| 3. | simple harmonic with amplitude \(\sqrt{a^2+b^{2}}.\) |
| 4. | simple harmonic with amplitude \(\dfrac{a+b}{2}\). |
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