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. \(\sqrt{\frac{qQ}{4 \pi \varepsilon_0 ~mR} }\)
2. \(\sqrt{\frac{qQ}{4 \pi \varepsilon_0 ~mR^2} }\)
3. \(\sqrt{\frac{qQ}{4 \pi \varepsilon_0 ~mR^3}}\)
4. \( \sqrt{\frac{m}{4 \pi \varepsilon_0 ~qQ} }\)
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.
2.
3.
4.
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 |
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. | \(a = 100 x^{3}\) |
Which of the following examples represent simple harmonic motion?
| 1. | The rotation of the earth about its axis. |
| 2. | The motion of an oscillating mercury column in a U-tube. |
| 3. | General vibrations of a polyatomic molecule about its equilibrium position. |
| 4. | A fan rotating with a constant angular velocity. |
From the given functions, identify the function which represents a periodic motion:
| 1. | \(e^{\omega t}\) | 2. | \(\text{log}_e(\omega t)\) |
| 3. | \(\text{sin}\omega t+ \text{cos}\omega t\) | 4. | \(e^{-\omega t}\) |
© 2024 GoodEd Technologies Pvt. Ltd.