Q. No.The rotation of the earth about its axis is:
1.
periodic motion.
2.
simple harmonic motion.
3.
periodic and simple harmonic motion.
4.
non-periodic motion.
A particle of mass \(m\) and charge \(\text-q\) moves diametrically through a uniformly charged sphere of radius \(R\) with total charge \(Q\). The angular frequency of the particle's simple harmonic motion, if its amplitude \(<R\), is given by:
1. \(\sqrt{\dfrac{qQ}{4 \pi \varepsilon_0 ~mR} }\)
2. \(\sqrt{\dfrac{qQ}{4 \pi \varepsilon_0 ~mR^2} }\)
3. \(\sqrt{\dfrac{qQ}{4 \pi \varepsilon_0 ~mR^3}}\)
4. \( \sqrt{\dfrac{m}{4 \pi \varepsilon_0 ~qQ} }\)
The figure shows the circular motion of a particle. The radius of the circle, the period, the sense of revolution, and the initial position are indicated in the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle \(P\) will be:
1. \(x \left( t \right) = B\) \(\text{sin} \left(\dfrac{2 πt}{30}\right)\)
2. \(x \left( t \right) = B\) \(\text{cos} \left(\dfrac{πt}{15}\right)\)
3. \(x \left( t \right) = B\) \(\text{sin} \left(\dfrac{πt}{15} + \dfrac{\pi}{2}\right)\)
4. \(x \left( t \right) = B\) \(\text{cos} \left(\dfrac{πt}{15} + \dfrac{\pi}{2}\right)\)
Displacement versus time curve for a particle executing SHM is shown in the figure. Choose the correct statement/s.
| 1. | Phase of the oscillator is the same at t =0 s and t = 2 s. |
| 2. | Phase of the oscillator is the same at t =2 s and t=6 s. |
| 3. | Phase of the oscillator is the same at t = 1 s and t=7 s. |
| 4. | Phase of the oscillator is the same at t=1 s and t=5 s. |
| 1. | 1, 2 and 4 | 2. | 1 and 3 |
| 3. | 2 and 4 | 4. | 3 and 4 |
For forced oscillations, a particle oscillates in a simple harmonic fashion with a frequency equal to:
1. the frequency of driving force.
2. the mean of frequency of driving force and natural frequency of the body.
3. the difference of frequency of driving force and natural frequency of the body.
4. the natural frequency of the body.
In damped oscillations, the damping force is directly proportional to the speed of the oscillator. If amplitude becomes half of its maximum value in 1 sec, then after 2 sec, the amplitude of the damped oscillation for which data is given, will be: (Initial amplitude = )
1.
2.
3.
4.
A particle is executing SHM with time period T. If the time period of its total mechanical energy is T', then will be:
| 1. | 2 | 2. | \(1 \over 2\) |
| 3. | Zero | 4. | Infinite |
Identify the correct definition:
| 1. | If after every certain interval of time, a particle repeats its motion, then the motion is called periodic motion. |
| 2. | To and fro motion of a particle is called oscillatory motion. |
| 3. | Oscillatory motion described in terms of single sine and cosine functions is called simple harmonic motion. |
| 4. | All of the above |
A spring having a spring constant of 1200 N/m is mounted on a horizontal table as shown in the figure. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released. The frequency of oscillations will be:
| 1. | \(3.0~\text{s}^{-1}\) | 2. | \(2.7~\text{s}^{-1}\) |
| 3. | \(1.2~\text{s}^{-1}\) | 4. | \(3.2~\text{s}^{-1}\) |
Which of the following relationships between the acceleration '\(a\)' and the displacement '\(x\)' of a particle involves simple harmonic motion?
| 1. | \(a = 0 . 7 x\) | 2. | \(a = - 200 x^{2} \) |
| 3. | \(a = - 10 x\) | 4. | \(a = 100 x^{3}\) |
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