Q. No.Two springs of spring constants \(k_1\) and \(k_2\) are joined in series. The effective spring constant of the combination is given by:
1. \(\frac{k_1+k_2}{2}\)
2. \(k_1+k_2\)
3. \(\frac{k_1k_2}{k_1+k_2}\)
4. \(\sqrt{k_1k_2}{}\)
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If two identical springs, each with a spring constant \(k,\) are connected in series, the new spring constant and time period will change by a factor of:
| 1. | \( \dfrac{1}{2},~ \sqrt{2} \) | 2. | \( \dfrac{1}{4},~ \sqrt{2} \) |
| 3. | \( \dfrac{1}{4},~ 2 \sqrt{2} \) | 4. | \( \dfrac{1}{2},~ 2 \sqrt{2} \) |
Two identical springs of spring constant \(k\) are attached to a block of mass \(m\) and to fixed supports as shown in the figure. When the mass is displaced from its equilibrium position on either side, it executes a simple harmonic motion. The period of oscillations is:
1. \(2 \pi \sqrt{\dfrac{{m}}{4{k}}}\)
2. \(2 \pi \sqrt{\dfrac{2{m}}{{k}}}\)
3. \(2 \pi \sqrt{\dfrac{{m}}{2{k}}}\)
4. \(2 \pi \sqrt{\dfrac{{m}}{{k}}}\)
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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 maximum acceleration of the mass is:
| 1. | \(6\) ms–2 | 2. | \(8\) ms–2 |
| 3. | \(3.3\) ms–2 | 4. | \(5.1\) ms–2 |
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What is the period of oscillation of the block shown in the figure?
| 1. | \(2\pi \sqrt{\dfrac{M}{k}}\) | 2. | \(2\pi \sqrt{\dfrac{4M}{k}}\) |
| 3. | \(\pi \sqrt{\dfrac{M}{k}}\) | 4. | \(2\pi \sqrt{\dfrac{M}{2k}}\) |
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1. \(3\)
2. \(4\)
3. \(2\)
4. \(1\)
1. \(20k\)
2. \(40k\)
3. \(k/2\)
4. none of these
1. \(k\)
2. \(2k\)
3. \(\dfrac k2\)
4. zero
| 1. | \(\pi \sqrt{\dfrac{4 m}{5 k}}\) | 2. | \(\pi \sqrt{\dfrac{6 m}{5 k}}\) |
| 3. | \(\pi \sqrt{\dfrac{12m}{5 k}}\) | 4. | \(\pi \sqrt{\dfrac{8m}{5 k}}\) |
Three masses, \(700~\text{g},\) \(500~\text{g},\) and \(400~\text{g}\) are suspended vertically from a spring and are in equilibrium. When the \(700~\text{g}\) mass is detached, the remaining system oscillates with a time period of \(3~\text{s}.\) If the \(500~\text{g}\) mass is also removed, what will be the new time period of oscillation?
| 1. | \(1~\text{s}\) | 2. | \(2~\text{s}\) |
| 3. | \(3~\text{s}\) | 4. | \(4~\text{s}\) |
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