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Q. No.A light rod \(AB\) is hinged at \(A\) so that it is free to rotate about \(A.\) It is initially horizontal with a small block of mass \(m\) attached at \(B,\) and a spring (constant - \(k\)) holding it vertically up at its mid-point. The time period of vertical oscillations of the system is:
| 1. | \(2 \pi \sqrt{\dfrac{m}{k}} \) | 2. | \(\pi \sqrt{\dfrac{m}{k}} \) |
| 3. | \(4\pi \sqrt{\dfrac{m}{k}}\) | 4. | \(\dfrac{\pi}{2} \sqrt{\dfrac{m}{k}}\) |
Subtopic: Â Spring mass system |
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The energy of the block is \(E\), and the plane is smooth, the wall at the end \(B\) is smooth. Collisions with walls are elastic. The distance \(AB=l\), the spring is ideal and the spring constant is \(k\). The time period of the motion is:
| 1. | \(2\pi\sqrt{\dfrac{m}{k}}\) |
| 2. | \(\pi\sqrt{\dfrac{m}{k}}+l\sqrt{\dfrac{2m}{E}}\) |
| 3. | \(2\pi\sqrt{\dfrac{m}{k}}+2l\sqrt{\dfrac{2m}{E}}\) |
| 4. | \(\pi\sqrt{\dfrac{m}{k}}+l\sqrt{\dfrac{m}{2E}}\) |
Subtopic: Â Spring mass system |
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A spring-mass system is undergoing horizontal oscillations on a frictionless surface. During the oscillation, the block picks up a particle, when it is at its extreme position. As a result of this,
| 1. | the amplitude increases. |
| 2. | the amplitude decreases. |
| 3. | the frequency increases. |
| 4. | the frequency decreases. |
Subtopic: Â Spring mass system |
 55%
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A block \(A\) is placed on a spring and causes it to be compressed; when another block \(B\) is placed on top of the first one the compression increases by \(125\%.\) The time period of small oscillations is \(T_A\) when \(A\) is present, and is \(T_{AB},\) when both \(A~\&~B\) are present. Then,
| 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. | \(T_{AB}=\dfrac{2}{3}~T_A\) |
Subtopic: Â Spring mass system |
 56%
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A block of mass \(m\) is pushed towards a spring of spring constant \(k,\) with a speed \(u.\) It is very close to the spring, initially. After a time \(t,\) the block rebounds and returns to its initial position. If \(u\) is increased, then:
| 1. | \(t\) increases. |
| 2. | \(t\) decreases. |
| 3. | \(t\) remains unchanged. |
| 4. | the effect on \(t\) cannot be determined due to insufficient information. |
Subtopic: Â Spring mass system |
 59%
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Two springs are joined end-to-end and connected to a block of mass \(m.\) The angular frequency \((\omega)\) of oscillation is:
| 1. | \(\sqrt{\dfrac{2k}{3m}}\) | 2. | \(\sqrt{\dfrac{3k}{2m}}\) |
| 3. | \(\sqrt{\dfrac{3k}{m}}\) | 4. | \(\sqrt{\dfrac{k}{3m}}\) |
Subtopic: Â Spring mass system |
 70%
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A block of mass \(m\) is connected to two springs of stiffness \(k,\) as shown in the figure. The effective spring constant, when these are replaced by a single spring, is:
| 1. | \(0\) | 2. | \(2k\) |
| 3. | \(\dfrac k2\) | 4. | infinity |
Subtopic: Â Spring mass system |
 72%
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A pendulum-bob \(A,\) after being released as shown, strikes a spring-block system when the bob \(A\) reaches its lowest position; the mass of the bob \(A\) being equal to that of the block (i.e., \(m\)) and the stiffness of the spring being \(k.\) The collision between the block and the bob \((A)\) is elastic. The time period of one complete oscillation is:
| 1. | \(2\pi{\Large\sqrt\frac{l}{g}}+2\pi{\Large\sqrt\frac{m}{k}} \) | 2. | \(\pi{\Large\sqrt\frac{l}{g}}+\pi{\Large\sqrt\frac{m}{k}}\) |
| 3. | \({\Large\sqrt\frac{g}{l}}+{\Large\sqrt\frac{k}{m}}\) | 4. | \(\Large\frac{1}{2\pi}\sqrt{\frac gl}+\frac{1}{2\pi}\sqrt\frac{k}{m}\) |
Subtopic: Â Spring mass system |
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A spring-mass system is undergoing small oscillations of amplitude \(A.\) When the block is at its mean position, it is given an impulse \(J\) in the direction of its motion, and its new amplitude is \(A'.\) Then, (given \(\alpha,\beta,\gamma\) are constants)
1. \(A'=A+\alpha J\)
2. \(A'^{\Large^2}=A^2+\alpha J^2\)
3. \(A'^{\Large^2}=A^2+\alpha J+\beta A\)
4. \(A'^{\Large^2}=A^2+\alpha J^2+\beta AJ\)
1. \(A'=A+\alpha J\)
2. \(A'^{\Large^2}=A^2+\alpha J^2\)
3. \(A'^{\Large^2}=A^2+\alpha J+\beta A\)
4. \(A'^{\Large^2}=A^2+\alpha J^2+\beta AJ\)
Subtopic: Â Spring mass system |
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