Q. No.Three particles of equal mass are connected by massless rods of length \(L\) to form an equilateral triangle, \(ABC.\) This triangle is pivoted at \(A\) and allowed to oscillate in its own plane. The time period of small oscillation is:
1.
\(2\pi\sqrt{\dfrac{L}{g}}\)
2.
\(2\pi\sqrt{\dfrac{2L}{g}}\)
3.
\(2\pi\sqrt{\dfrac{L}{2g}}\)
4.
\(2\pi\sqrt{\dfrac{2L}{\sqrt3g}}\)
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| 1. | \(T\) | 2. | \(\pi T\) |
| 3. | \(\pi\sqrt2T\) | 4. | \(\dfrac{\pi}{\sqrt 2}T\) |
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| 1. | \(T_{AB}=\dfrac{3}{2}~T_A\) | 2. | \(T_{AB}=\dfrac{\sqrt5}{2}~T_A\) |
| 3. | \(T_{AB}=\dfrac{1}{2}~T_A\) | 4. | \(T_{AB}=\dfrac{2}{3}~T_A\) |
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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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| 1. | uniform circular motion |
| 2. | elliptical motion |
| 3. | linear SHM |
| 4. | angular SHM along a circle |
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| 1. | \(t\) increases. |
| 2. | \(t\) decreases. |
| 3. | \(t\) remains unchanged. |
| 4. | the effect on \(t\) cannot be determined due to insufficient information. |
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| 1. | \(\sqrt{\dfrac{2k}{3m}}\) | 2. | \(\sqrt{\dfrac{3k}{2m}}\) |
| 3. | \(\sqrt{\dfrac{3k}{m}}\) | 4. | \(\sqrt{\dfrac{k}{3m}}\) |
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Their time periods are related as:
1. \(T_A\Big(1+\dfrac{1}{1000}\Big)=T_B\)
2. \(T_B\Big(1+\dfrac{1}{1000}\Big)=T_A\)
3. \(T_A\Big(1+\dfrac{1}{2000}\Big)=T_B\)
4. \(T_B\Big(1+\dfrac{1}{2000}\Big)=T_A\)
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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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\(x=A+A\text{sin}\omega t\\ y=A-A\text{sin}\omega t\)
are superposed on a particle, along \(x\) and \(y\) directions. The resultant of these motions is:
| 1. | circular motion |
| 2. | SHM along \(x\)-axis |
| 3. | SHM along \(y\)-axis |
| 4. | SHM, but along a direction other than \(x\) or \(y\)-axis |
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