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 |
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. |
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 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. \( \sqrt{\dfrac{m}{4 \pi \varepsilon_0 ~qQ} }\)
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. |
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 |
A particle executing SHM crosses points A and B with the same velocity. Having taken 3 s in passing from A to
B, it returns to B after another 3 s. The time period of the SHM will be:
1. | 15 s | 2. | 6 s |
3. | 12 s | 4. | 9 s |