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Q. No.For a simple pendulum having a time period, \(T,\) the variation of kinetic energy \((K.E.)~\) with time \((t)~\) is represented by:
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Subtopic: Energy of SHM |
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Savitha, a XI standard student, while conducting an experiment to determine the effective length of a simple pendulum \(L,\) notes down the data of time taken to complete \(30\) oscillations as \(60\) s and hence calculates the length of the simple pendulum as:
(take \(\pi^2 = 9.8\) and \(g = 9.8 \text{ m/s}^2\))
1. \(2~\text{m}\)
2. \(0.75~\text{m}\)
3. \(1.5~\text{m}\)
4. \(1~\text{m}\)
(take \(\pi^2 = 9.8\) and \(g = 9.8 \text{ m/s}^2\))
1. \(2~\text{m}\)
2. \(0.75~\text{m}\)
3. \(1.5~\text{m}\)
4. \(1~\text{m}\)
Subtopic: Angular SHM |
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The sum of kinetic energy and potential energy of a simple pendulum bob is \(0.02\) joules. The speed of the simple pendulum bob at equilibrium position is approximately:
(consider mass of the bob \(=20~\text{g}\))
1. \(1.41~\text{m/s }\)
2. \(14.1~\text{m/s }\)
3. \(0.2~\text{m/s }\)
4. \(2.0~\text{m/s }\)
(consider mass of the bob \(=20~\text{g}\))
1. \(1.41~\text{m/s }\)
2. \(14.1~\text{m/s }\)
3. \(0.2~\text{m/s }\)
4. \(2.0~\text{m/s }\)
Subtopic: Energy of SHM |
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In an oscillating spring mass system, a spring is connected to a box filled with the sand. As the box oscillates, sand leaks slowly out of the box vertically so that the average frequency \(\omega~(t)\) and average amplitude \(A~(t)\) of the system changes with time \(t.\) Which of the following options systemically depicts these changes correctly?
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4. |  |
Subtopic: Spring mass system |
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Two identical point masses \(P\) and \(Q,\) suspended from two separate massless springs of spring constant \(k_1\) and \(k_2,\) respectively, oscillate vertically. If their maximum speeds are the same, the ratio \(\left(\dfrac{A_Q}{A_P} \right)\) of the amplitude \(A_Q\) of mass \(Q \) to the amplitude \(A_P\) of mass \(P\) is:
| 1. | \(\sqrt{\dfrac{k_2}{k_1}}\) | 2. | \(\sqrt{\dfrac{k_1}{k_2}}\) |
| 3. | \(\dfrac{k_2}{k_1}\) | 4. | \(\dfrac{k_1}{k_2}\) |
Subtopic: Spring mass system |
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If \(x = 5 \mathrm {sin }\left(\pi t+ {\dfrac {\pi} 3}\right)~\text m\) represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively are:
| 1. | \(5~\text m, 2~\text s\) | 2. | \(5~\text {cm}, 1~\text s\) |
| 3. | \(5~\text m, 1~\text s\) | 4. | \(5~\text {cm}, 2~\text s\) |
Subtopic: Simple Harmonic Motion |
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If the mass of a bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is \( \dfrac{x}{2}\) times its original time period. The value of \(x\) is:
| 1. | \(\sqrt2\) | 2. | \(2\sqrt3\) |
| 3. | \(4\) | 4. | \(\sqrt3\) |
Subtopic: Angular SHM |
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If \(T_1,T_2,T_3,T_4\) and \(T_5\) represent the tension in the string of a simple pendulum when the bob is at the left extreme, right extreme, mean, any intermediate left and any intermediate right positions, respectively. Then, which of the following relations are correct?
Choose the most appropriate answer from the options given below:
| (A) | \(T_1=T_2\) | (B) | \(T_3>T_2\) |
| (C) | \(T_4>T_3\) | (D) | \(T_3=T_4\) |
| (E) | \(T_5>T_2\) | ||
| 1. | (A), (B) and (C) only | 2. | (B), (C) and (D) only |
| 3. | (A), (B) and (E) only | 4. | (C), (D) and (E) only |
Subtopic: Angular SHM |
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A particle executing simple harmonic motion with amplitude \(A\) has the same potential and kinetic energies at the displacement:
| 1. | \(2\sqrt{A}\) | 2. | \(\dfrac{A}{2}\) |
| 3. | \(\dfrac{\mathrm{A}}{\sqrt{2}}\) | 4. | \(A\sqrt{2}\) |
Subtopic: Energy of SHM |
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The two-dimensional motion of a particle, described by \(\vec{r}=(\hat{i}+2\hat{j}) A~\text{cos}(\omega t) \) is a/an:
Choose the correct answer from the options given below:
| (A) | parabolic path |
| (B) | elliptical path |
| (C) | periodic motion |
| (D) | simple harmonic motion |
Choose the correct answer from the options given below:
| 1. | (B), (C), and (D) only |
| 2. | (A), (B), and (C) only |
| 3. | (A), (C), and (D) only |
| 4. | (C) and (D) only |
Subtopic: Types of Motion |
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