- 1(current)
Q. No.The radius of the circle, the period of revolution, initial position and direction of revolution are indicated in the figure.
The \(y\)-projection of the radius vector of rotating particle \(P\) will be:
| 1. | \(y(t)=3 \cos \left(\dfrac{\pi \mathrm{t}}{2}\right)\), where \(y\) in m |
| 2. | \(y(t)=-3 \cos 2 \pi t\) , where \(y\) in m |
| 3. | \(y(t)=4 \sin \left(\dfrac{\pi t}{2}\right)\), where \(y\) in m |
| 4. | \(y(t)=3 \cos \left(\dfrac{3 \pi \mathrm{t}}{2}\right) \), where \(y\) in m |
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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 \({x\text-}\)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. \(x \left( t \right) = B\text{cos} \left(\dfrac{πt}{15} + \dfrac{\pi}{2}\right)\)
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The displacement \( x\) of a particle varies with time \(t\) as \(x = A sin\left (\frac{2\pi t}{T} +\frac{\pi}{3} \right)\). The time taken by the particle to reach from \(x = \frac{A}{2} \) to \(x = -\frac{A}{2} \) will be:
| 1. | \(\frac{T}{2}\) | 2. | \(\frac{T}{3}\) |
| 3. | \(\frac{T}{12}\) | 4. | \(\frac{T}{6}\) |
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- 1(current)
Q. No.
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