Q. No.| 1. | \(v_0\) | 2. | \(2v_0\) |
| 3. | \({\dfrac{\sqrt3}{2}}v_0\) | 4. | \(\sqrt3v_0\) |
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| 1. | \({\Large\frac{1}{2}}kA^2\) | 2. | \(kA^2\) |
| 3. | \(2kA^2\) | 4. | \(4kA^2\) |
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| (A) | \(x=A\sin^2\omega t\) |
| (B) | \(x=A\sin\omega t+B\cos2\omega t\) |
| (C) | \(x=A\sin^2\omega t+B\cos2\omega t\) |
2. A and B
3. A and C
4. A, B and C
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A uniform rod of length \(l\) is suspended by an end and is made to undergo small oscillations. The time period of small oscillation is \(T\). Then, the acceleration due to gravity at this place is:
| 1. | \(4\pi^2\dfrac{l}{T^2}\) | 2. | \(\dfrac{4\pi^2}{3}\dfrac{l}{T^2}\) |
| 3. | \(\dfrac{8\pi^2}{3}\dfrac{l}{T^2}\) | 4. | \(\dfrac{12\pi^2l}{T^2}\) |
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| 1. | \(2 \pi \sqrt{\dfrac{m}{k}} \) | 2. | \(\pi \sqrt{\dfrac{m}{k}} \) |
| 3. | \(4\pi \sqrt{\dfrac{m}{k}}\) | 4. | \(\dfrac{\pi}{2} \sqrt{\dfrac{m}{k}}\) |
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| Statement I: | If the acceleration of a particle is directed towards a fixed point, and proportional to the distance from that point – the motion is SHM. |
| Statement II: | During SHM, the kinetic energy of the particle oscillates at twice the frequency of the SHM. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
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1. \(5\) cm/s
2. \(10\) cm/s
3. at least \(10\) cm/s
4. at most \(10\) cm/s
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| 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. | \(\begin{aligned} 2\large{\sqrt\frac{h}{g}} & \\ \end{aligned}\) |
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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 \(A\). |
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1. \(\Large\sqrt{\frac{4L\sin\theta}{g}}\)
2. \(\Large\sqrt{\frac{8L\sin\theta}{g}}\)
3. \(\Large\sqrt{\frac{8L}{g\sin\theta}}\)
4. \(\Large\sqrt{\frac{4L}{g\sin\theta}}\)
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