- 1(current)
Q. No.Which, of the following, represents the displacement in simple harmonic motion?
| (A) | \(x=A\sin^2\omega t\) |
| (B) | \(x=A\sin\omega t+B\cos2\omega t\) |
| (C) | \(x=A\sin^2\omega t+B\cos2\omega t\) |
| 1. | A only | 2. | A and B |
| 3. | A and C | 4. | A, B and C |
Subtopic: Â Types of Motion |
Level 4: Below 35%
Hints
Two SHMs given by their displacements along the respective directions are superposed: \(x=A\sin\omega t~~~~(1^{\text{st}}~\text{SHM along }x\text{-axis})\\ y=A\sin\bigg(\omega t+{\large\frac{\pi}{2}}\bigg)~~~~(2^{\text{nd}}~\text{SHM along }y\text{-axis}).\)
The resultant motion is:
The resultant motion is:
| 1. | SHM along a straight line |
| 2. | SHM along a circular arc |
| 3. | uniform circular motion |
| 4. | motion along an elliptic path |
Subtopic: Â Types of Motion |
Level 3: 35%-60%
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Trains travel between station \(A\) and station \(B\): on the way up (from \(A~\text{to}~B\)) - they travel at a speed of \(80\) km/h, while on the return trip the trains travel at twice that speed. The services are maintained round the clock. Trains leave station \(A\) every \(30\) min for station \(B\) and reach \(B\) in \(2\) hrs. All trains operate continuously, without any rest at \(A\) or \(B\).
| 1. | the frequency of trains leaving \(B\) must be twice as much as \(A\). |
| 2. | the frequency of trains leaving \(B\) must be half as much as \(A\). |
| 3. | the frequency of trains leaving \(B\) is equal to that at \(A\). |
| 4. | the situation is impossible to maintain unless larger number of trains are provided at \(A\). |
Subtopic: Â Types of Motion |
Level 3: 35%-60%
Hints
An elastic ball rebounds vertically to a height \(h\) above the ground, the period of its motion will be:
| 1. | \(\begin{aligned} \large\sqrt\frac{2h}{g} & \\ \end{aligned}\) | 2. | \(\begin{aligned} \large\sqrt\frac{8h}{g} & \\ \end{aligned}\) |
| 3. | \(\begin{aligned} \large\sqrt\frac{h}{2g} & \\ \end{aligned}\) | 4. | \(\begin{aligned} 2\large{\sqrt\frac{h}{g}} & \\ \end{aligned}\) |
Subtopic: Â Types of Motion |
Level 3: 35%-60%
Hints
- 1(current)
Q. No.
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