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Q. No.\((\text{sin}\omega t+\text{cos}\omega t)\) is a periodic function, its time period will be:
1.
\(\dfrac{\pi}{\omega}\)
2.
\(\dfrac{2\pi}{\omega}\)
3.
\(\dfrac{1}{\omega}\)
4.
\(\dfrac{\omega}{2\pi}\)
Subtopic: Types of Motion |
86%
Level 1: 80%+
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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 |
83%
Level 1: 80%+
NEET - 2022
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The restoring force of a spring, with a block attached to the free end of the spring, is represented by:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Spring mass system |
70%
Level 2: 60%+
NEET - 2022
Hints
Match List-I with List-II.
Choose the correct answer from the options given below:
| List-I (\(x \text{-}y\) graphs) |
List-II (Situations) |
||
| (a) |  |
(i) | Total mechanical energy is conserved |
| (b) |  |
(ii) | Bob of a pendulum is oscillating under negligible air friction |
| (c) |  |
(iii) | Restoring force of a spring |
| (d) |  |
(iv) | Bob of a pendulum is oscillating along with air friction |
Choose the correct answer from the options given below:
| (a) | (b) | (c) | (d) | |
| 1. | (iv) | (ii) | (iii) | (i) |
| 2. | (iv) | (iii) | (ii) | (i) |
| 3. | (i) | (iv) | (iii) | (ii) |
| 4. | (iii) | (ii) | (i) | (iv) |
Subtopic: Energy of SHM |
86%
Level 1: 80%+
NEET - 2022
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A simple pendulum is oscillating with an angular frequency \(\omega\) and amplitude \(A.\) The displacement and velocity of the pendulum, when potential energy is half the total energy, are given by:
| 1. | \(\dfrac{A}{\sqrt{2}}, \dfrac{A}{\sqrt{2}} \omega\) | 2. | \(\dfrac{A}{2}, \dfrac{A}{2} \omega\) |
| 3. | \(\sqrt2A, 2A \omega\) | 4. | \(\sqrt2A, \sqrt2A \omega\) |
Subtopic: Energy of SHM |
86%
Level 1: 80%+
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A body of mass \(4~\text{kg}\) is executing SHM. Its potential energy varies with \(x\) as; \(U=\left [ \left ( x-2 \right )^{2}+20 \right ]~\text J.\) If the total energy of the body is \(70~\text J,\) its maximum speed is:
1. \(\sqrt{23}~\text{m/s}\)
2. \(\sqrt{25}~\text{m/s}\)
3. \(\sqrt{27}~\text{m/s}\)
4. \(\sqrt{35} ~\text{m/s}\)
1. \(\sqrt{23}~\text{m/s}\)
2. \(\sqrt{25}~\text{m/s}\)
3. \(\sqrt{27}~\text{m/s}\)
4. \(\sqrt{35} ~\text{m/s}\)
Subtopic: Energy of SHM |
58%
Level 3: 35%-60%
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The time period of a simple pendulum in a stationary lift is \(T.\) If the lift accelerates upward with an acceleration of \(\dfrac g 6\) (where \(g\) is the acceleration due to gravity), then the time period of the pendulum would be:
| 1. | \(\sqrt{\dfrac{6}{5}} ~T \) | 2. | \(\sqrt{\dfrac{5}{6}} ~T\) |
| 3. | \(\sqrt{\dfrac{6}{7}}~T\) | 4. | \(\sqrt{\dfrac{7}{6}} ~T\) |
Subtopic: Angular SHM |
80%
Level 1: 80%+
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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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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 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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