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Q. No.An electric motor of mass \(40~\text{kg}\) is mounted on four vertical springs each having a spring constant of \(4000~\text{N/m}.\) The period with which the motor vibrates vertically is:
1.
\(0.314~\text s\)
2.
\(3.14~\text s\)
3.
\(0.628~\text s\)
4.
\(0.157~\text s\)
Subtopic: Combination of Springs |
64%
Level 2: 60%+
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If a simple pendulum be suspended in an elevator which is moving upward, its time period is found to decrease by \(2\%.\) The acceleration of the elevator is (in magnitude):
1. \(2\%\) of \(g\)
2. \(1\%\) of \(g\)
3. \(4\%\) of \(g\)
4. \(102\%\) of \(g\)
1. \(2\%\) of \(g\)
2. \(1\%\) of \(g\)
3. \(4\%\) of \(g\)
4. \(102\%\) of \(g\)
Subtopic: Angular SHM |
77%
Level 2: 60%+
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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 |
80%
Level 1: 80%+
NEET - 2022
Hints
Given below are two statements:
| Assertion (A): | The combination of \(y=\text{sin}\omega t+\text{cos}2\omega t\) is not a simple harmonic function even though it is periodic. |
| Reason (R): | All periodic functions satisfy the relation \( \dfrac{d^{2} y}{d t^{2}}=-k y \). |
| 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. | Both (A) and (R) are False. |
Subtopic: Simple Harmonic Motion |
Level 3: 35%-60%
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A particle executes simple harmonic motion between \(x=-A\) and \(x=+A.\) The time taken for it to move from \(0\) to \(A/2\) is \(T_1\) and the time to move from \(A/2\) to \(A\) is \(T_2.\) Then:
1. \(T_{1}<T_{2}\)
2. \(T_{1}>T_{2}\)
3. \(T_{1}=T_{2}\)
4. \(T_{1}=2 T_{2}\)
1. \(T_{1}<T_{2}\)
2. \(T_{1}>T_{2}\)
3. \(T_{1}=T_{2}\)
4. \(T_{1}=2 T_{2}\)
Subtopic: Linear SHM |
74%
Level 2: 60%+
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A body is performing simple harmonic motion with an amplitude of \(10~\text{cm}.\) The velocity of the body was tripled by air jet when it is at \(5~\text{cm}\) from its mean position. The new amplitude of vibration is \(\sqrt x~\text{cm}.\) The value of \(x \) is:
| 1. | \(500\) | 2. | \(600\) |
| 3. | \(700\) | 4. | \(800\) |
Subtopic: Simple Harmonic Motion |
66%
Level 2: 60%+
JEE
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A block of mass \(M\) is connected to a spring constant \(k.\) It oscillates on the frictionless inclined surface as shown in the figure. The time period of oscillation is:
| 1. | \(T=2 \pi \sqrt{\dfrac{M}{k}}\) | 2. | \(T=2 \pi \sqrt{\dfrac{k}{M}}\) |
| 3. | \(T=\dfrac{1}{2 \pi} \sqrt{\dfrac{k}{M}}\) | 4. | \(T=2 \pi \sqrt{\dfrac{M}{k}} \sin \theta\) |
Subtopic: Spring mass system |
81%
Level 1: 80%+
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A body executing SHM has a maximum speed of \(30~\text{cm s}^{-1}\) and a maximum acceleration of \(60~\text{cm s}^{-2}.\) What is the time period of the oscillating body in seconds?
| 1. | \(\pi\) | 2. | \(\pi/2\) |
| 3. | \(2\pi\) | 4. | \(\pi/4\) |
Subtopic: Simple Harmonic Motion |
90%
Level 1: 80%+
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On average, a human heart is found to beat \(72\) times per minute. The frequency of heartbeat will be:
1. \(0.833~\text s^{-1}\)
2. \(1.2~\text s^{-1}\)
3. \(12~\text s^{-1}\)
4. \(72~\text s^{-1}\)
1. \(0.833~\text s^{-1}\)
2. \(1.2~\text s^{-1}\)
3. \(12~\text s^{-1}\)
4. \(72~\text s^{-1}\)
Subtopic: Types of Motion |
72%
Level 2: 60%+
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A body oscillates with simple harmonic motion according to the equation (in SI units),
\(x=5 \cos \left(2 \pi t+\dfrac{\pi}{3}\right) \)
The displacement of the body at a time \(t=1.5~\text s\) is:
1. \(-5~\text m\)
2. \(-2.5~\text m\)
3. \(-2.0~\text m\)
4. \(-1.0~\text m\)
\(x=5 \cos \left(2 \pi t+\dfrac{\pi}{3}\right) \)
The displacement of the body at a time \(t=1.5~\text s\) is:
1. \(-5~\text m\)
2. \(-2.5~\text m\)
3. \(-2.0~\text m\)
4. \(-1.0~\text m\)
Subtopic: Simple Harmonic Motion |
79%
Level 2: 60%+
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