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Q. No.A particle moves in a plane such that its displacements are the sum of two displacements \(\overrightarrow {r_1}\) , and \(\overrightarrow {r_2};\) each of which undergo SHM in opposite phase with respect to the other, but of unequal amplitude. The resultant motion of the particle is:
1.
uniform circular motion
2.
elliptical motion
3.
linear SHM
4.
angular SHM along a circle
Subtopic: Simple Harmonic Motion |
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Two pendulums of length \(121\) cm and \(100\) cm start vibrating in phase. At some instant, the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at the mean position is:
| 1. | \(8\) | 2. | \(11\) |
| 3. | \(9\) | 4. | \(10\) |
Subtopic: Angular SHM |
67%
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During simple harmonic motion of a body, the energy at the extreme position is:
| 1. | both kinetic and potential |
| 2. | is always zero |
| 3. | purely kinetic |
| 4. | purely potential |
Subtopic: Energy of SHM |
78%
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Two identical simple pendulums are compared, one \((A)\) located on the surface of the earth and the other \((B)\) – at a height \((h)\) above the earth's surface: \(h=\frac{R}{1000}.\)
Their time periods are related as:
1. \(T_A\Big(1+\frac{1}{1000}\Big)=T_B\)
2. \(T_B\Big(1+\frac{1}{1000}\Big)=T_A\)
3. \(T_A\Big(1+\frac{1}{2000}\Big)=T_B\)
4. \(T_B\Big(1+\frac{1}{2000}\Big)=T_A\)
Their time periods are related as:
1. \(T_A\Big(1+\frac{1}{1000}\Big)=T_B\)
2. \(T_B\Big(1+\frac{1}{1000}\Big)=T_A\)
3. \(T_A\Big(1+\frac{1}{2000}\Big)=T_B\)
4. \(T_B\Big(1+\frac{1}{2000}\Big)=T_A\)
Subtopic: Angular SHM |
58%
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A particle undergoes SHM with an amplitude of \(10\) cm and a time period of \(4\) s. The average velocity of the particle during the course of its motion from its mean position to its extreme position is:
1. \(5\) cm/s
2. \(10\) cm/s
3. at least \(10\) cm/s
4. at most \(10\) cm/s
1. \(5\) cm/s
2. \(10\) cm/s
3. at least \(10\) cm/s
4. at most \(10\) cm/s
Subtopic: Simple Harmonic Motion |
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Two SHMs of the form:
\(x=A+Asin\omega t\\ y=A-Asin\omega t\)
are superposed on a particle, along \(x\) and \(y\) directions. The resultant of these motions is:
\(x=A+Asin\omega t\\ y=A-Asin\omega t\)
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 |
Subtopic: Simple Harmonic Motion |
52%
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Given below are two statements:
| Statement I: | If the acceleration of a particle is directed towards a fixed point, and proportional to the distance from that point – the motion is SHM. |
| Statement II: | During SHM, the kinetic energy of the particle oscillates at twice the frequency of the SHM. |
| 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. |
Subtopic: Energy of SHM |
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A particle executes SHM along a straight line.
| 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. |
Subtopic: Simple Harmonic Motion |
70%
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The effective spring constant in calculating the time period of SHM of the system of springs and the block is:
1. \((k_1+k_2)\)
2. \(|k_1-k_2|\)
3. \(\Big(\frac{1}{k_1}+\frac{1}{k_2}\Big)^{-1}\)
4. \(\Big|\frac{1}{k_1}-\frac{1}{k_2}\Big|^{-1}\)
1. \((k_1+k_2)\)
2. \(|k_1-k_2|\)
3. \(\Big(\frac{1}{k_1}+\frac{1}{k_2}\Big)^{-1}\)
4. \(\Big|\frac{1}{k_1}-\frac{1}{k_2}\Big|^{-1}\)
Subtopic: Spring mass system |
79%
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Identify the function which represents a non-periodic motion?
| 1. | \(e^{-\omega t}\) | 2. | \(\text{sin}\omega t\) |
| 3. | \(\text{sin}\omega t+\text{cos}\omega t\) | 4. | \(\text{sin}(\omega t+\pi/4)\) |
Subtopic: Types of Motion |
81%
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