# 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.

Subtopic:  Types of Motion |
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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. $$\sqrt{\dfrac{m}{4 \pi \varepsilon_0 ~qQ} }$$

Subtopic:  Linear SHM |
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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 $$\mathrm{x\text-}$$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. $$x \left( t \right) = B$$ $$\text{cos} \left(\dfrac{πt}{15} + \dfrac{\pi}{2}\right)$$

Subtopic:  Simple Harmonic Motion | Phasor Diagram |
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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
Subtopic:  Simple Harmonic Motion |
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A particle is executing SHM with time period T. If the time period of its total mechanical energy is T', then $\frac{{T}^{\text{'}}}{T}$ will be:

 1 2 2 $$1 \over 2$$ 3 Zero 4 Infinite
Subtopic:  Energy of SHM |
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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

Subtopic:  Types of Motion |
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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 $$3.2~\text{s}^{-1}$$
Subtopic:  Spring mass system |
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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. $$a = 100 x^{3}$$

Subtopic:  Simple Harmonic Motion |
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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.
Subtopic:  Simple Harmonic Motion |
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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 $$e^{-\omega t}$$

Subtopic:  Types of Motion |
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NEET - 2020
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