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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: Â Simple Harmonic Motion |
Level 3: 35%-60%
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A particle moves in a plane such that its displacements are the sum of two displacements \(\vec{ r}_1\), and \(\vec{r}_2;\) 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: Â Simple Harmonic Motion |
Level 3: 35%-60%
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A particle is subjected to two SHMs, one along the \(x\text-\)axis and the other along the \(y\text-\)axis:
\(x=A\sin\omega t\\ y=A\sin(\omega t+\pi)\)
The resulting motion is:
\(x=A\sin\omega t\\ y=A\sin(\omega t+\pi)\)
The resulting motion is:
| 1. | Uniform circular motion. |
| 2. | Elliptic motion. |
| 3. | SHM along a straight line. |
| 4. | SHM along a circle. |
Subtopic: Â Simple Harmonic Motion |
Level 3: 35%-60%
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Two SHMs of the form:
\(x=A+A\text{sin}\omega t\\ y=A-A\text{sin}\omega t\)
are superposed on a particle, along \(x\) and \(y\) directions. The resultant of these motions is:
\(x=A+A\text{sin}\omega t\\ y=A-A\text{sin}\omega t\)
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 |
Subtopic: Â Simple Harmonic Motion |
 54%
Level 3: 35%-60%
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If two SHMs of the same frequency and same amplitude are added but in opposite phase, then, their resultant will be:
| 1. | SHM of same frequency but double amplitude |
| 2. | SHM of double frequency but same amplitude |
| 3. | SHM of same frequency but smaller amplitude |
| 4. | no motion, due to cancellation |
Subtopic: Â Simple Harmonic Motion |
 59%
Level 3: 35%-60%
Hints
A particle is acted upon by two SHMs, one along the \(x\)-axis and the other along the \(y\)-axis: \(x=A\sin\omega t\\ y=A\cos(\omega t+90^\circ)\)
The resulting motion of the particle will be:
The resulting motion of the particle will be:
| 1. | SHM with amplitude \(A\) |
| 2. | SHM with amplitude \(\sqrt2A\) |
| 3. | Circular motion with a radius \(A\) |
| 4. | Circular motion with a radius \(\sqrt2A\) |
Subtopic: Â Simple Harmonic Motion |
 60%
Level 2: 60%+
Hints
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: Â Simple Harmonic Motion |
 77%
Level 2: 60%+
Hints
The graph represents the variation of the position of a particle \((x)\) as a function of time \((t);\) the variation being sinusoidal.
The amplitude of the motion of the particle is:
1. \(6~\text{cm}\)
2. \(3~\text{cm}\)
3. \(1.5~\text{cm}\)
4. \(12~\text{cm}\)
The amplitude of the motion of the particle is:
1. \(6~\text{cm}\)
2. \(3~\text{cm}\)
3. \(1.5~\text{cm}\)
4. \(12~\text{cm}\)
Subtopic: Â Simple Harmonic Motion |
 51%
Level 3: 35%-60%
Hints
The graph represents the variation of the position of a particle \((x)\) as a function of time \((t);\) the variation being sinusoidal.
The mean position of the particle is at:
1. \(x=0~\text{cm}\)
2. \(x=6~\text{cm}\)
3. \(x=3~\text{cm}\)
4. \(x=2~\text{cm}\)
The mean position of the particle is at:
1. \(x=0~\text{cm}\)
2. \(x=6~\text{cm}\)
3. \(x=3~\text{cm}\)
4. \(x=2~\text{cm}\)
Subtopic: Â Simple Harmonic Motion |
 64%
Level 2: 60%+
Hints
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