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)
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 \(t=\dfrac{T}{2}\) |
Which of the following functions of time represent/s periodic motion? [ω is any positive constant]
(a) sinωt + cosωt
(b) sinωt + cos2ωt + sin4ωt
(c) e–ωt
(d) log(ωt)
(e) sin2ωt
1. (a)
2. (a), (b) and (d)
3. (a), (b) and (e)
4. All
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
The displacement-time graph of a particle executing SHM is shown in the figure. Its displacement equation will be: (Time period = 2 second)
1.
2.
3.
4.
The velocity-time diagram of a harmonic oscillator is shown in the figure given below. The frequency of oscillation will be:
1. 25 Hz
2. 50 Hz
3. 12.25 Hz
4. 33.3 Hz
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. |
Assertion (A): | If a pendulum is suspended in a lift and lift is falling freely, then its time period becomes infinite. |
Reason (R): | Free falling body has acceleration equal to 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. |
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. |