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Q. No.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.
Subtopic: Types of Motion |
80%
Level 1: 80%+
Hints
The (displacement-time) graph of a particle executing SHM is shown in the figure. Then:
| (a) | the force is zero at \(t=\dfrac{3T}{4}\) |
| (b) | the acceleration is maximum at \(t=\dfrac{4T}{4}\) |
| (c) | the velocity is maximum at \(t=\dfrac{T}{4}\) |
| (d) | the potential energy is equal to the kinetic energy of oscillation at \(t=\dfrac{T}{2}\) |
| 1. | (a), (b) and (d) only | 2. | (a), (b) and (c) only |
| 3. | (b), (c) and (d) only | 4. | (c) and (d) only |
Subtopic: Simple Harmonic Motion |
68%
Level 2: 60%+
Hints
A body is performing SHM, then its:
| (a) | average total energy per cycle is equal to its maximum kinetic energy. |
| (b) | average kinetic energy per cycle is equal to half of its maximum kinetic energy. |
| (c) | mean velocity for a complete cycle is equal to \(\dfrac{2}{\pi}\) times of its maximum velocity. |
| (d) | root mean square velocity is \(\dfrac{1}{\sqrt{2}}\) times of its maximum velocity. |
Choose the correct alternatives:
1. (a), (b), (d)
2. (a), (c)
3. (b), (d)
4. (b), (c), (d)
Subtopic: Energy of SHM |
54%
Level 3: 35%-60%
Hints
The displacement-time graph of a particle executing SHM is shown in the figure. Its displacement equation will be: (Time period = \(2\) second)
1. \(x= 10\sin\left(\pi t+\frac{\pi}{6}\right)\)
2. \(x= 10\sin\left(\pi t\right)\)
3. \(x= 10\cos\left(\pi t\right)\)
4. \(x= 5\sin\left(\pi t+\frac{\pi}{6}\right)\)
Subtopic: Linear SHM |
65%
Level 2: 60%+
Hints
The velocity-time diagram of a harmonic oscillator is shown in the figure given below. The frequency of oscillation will be:
1. \(25~\text{Hz}\)
2. \(50~\text{Hz}\)
3. \(12.25~\text{Hz}\)
4. \(33.3~\text{Hz}\)
Subtopic: Simple Harmonic Motion |
75%
Level 2: 60%+
Hints
Which of the following functions of time represent/s periodic motion?
(\(\omega\) is any positive constant)
Choose the correct option from the given ones:
(\(\omega\) is any positive constant)
| (a) | \((\sin\omega t+ \cos \omega t)\) |
| (b) | \((\sin\omega t+ \cos 2\omega t+ \sin4\omega t)\) |
| (c) | \(e^{-\omega t}\) |
| (d) | \(\mathrm{log(\omega t)}\) |
| (e) | \(\sin^{2}\omega t\) |
Choose the correct option from the given ones:
| 1. | (a) only |
| 2. | (a), (b), and (d) only |
| 3. | (a), (b), and (e) only |
| 4. | All of these |
Subtopic: Types of Motion |
69%
Level 2: 60%+
Hints
Which of the following statements is/are correct.
| a. | Motion of a kink in a longitudinal spring produced by displacing one end of the spring sideways is transverse and longitudinal, both. |
| b. | Waves produced in a cylinder containing a liquid by moving its piston back and forth is longitudinal. |
| c. | Waves produced by a motorboat sailing in water are transverse and longitudinal, both. |
| d. | Ultrasonic waves in air produced by a vibrating quartz crystal are longitudinal. |
1. (a), (b) and (d)
2. (b) and (d)
3. (a), (c) and (d)
4. All are correct
Subtopic: Types of Motion |
64%
Level 2: 60%+
Hints
Given below are two statements:
| Assertion (A): | When a pendulum is made to oscillate on the surface of the moon, its time period increases. |
| Reason (R): | Moon is much smaller as compared to Earth. |
| 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: Angular SHM |
Level 3: 35%-60%
Hints
Given below are two statements:
| Assertion (A): | If a pendulum is suspended in a lift and the lift is falling freely, then its time period becomes infinite. |
| Reason (R): | The free-falling body has acceleration equal to the acceleration due to gravity. |
| 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: Angular SHM |
83%
Level 1: 80%+
Hints
Given below are two statements:
| Assertion (A): | The graph between velocity and displacement for a simple harmonic motion is an ellipse. |
| Reason (R): | Velocity does not change uniformly with displacement in simple harmonic motion. |
| 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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