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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.
\(2\pi\sqrt{\dfrac{2L}{\sqrt3g}}\)
Subtopic: Angular SHM |
54%
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An elastic ball is projected vertically upward with a speed \(u,\) and it returns to the ground and rebounds, the motion is periodic with a period \(T.\) A simple pendulum, having a length equal to maximum altitude attained by this ball, would have a time period of:
| 1. | \(T\) | 2. | \(\pi T\) |
| 3. | \(\pi\sqrt2T\) | 4. | \(\dfrac{\pi}{\sqrt 2}T\) |
Subtopic: Angular SHM |
52%
From NCERT
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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: Spring mass system |
56%
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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: Spring mass system |
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A particle moves in a plane such that its displacements are the sum of two displacements \(\vec{ r}_1\), and \(\vec{r}_2;\) each of which undergo SHM in opposite phase with respect to the other, but of unequal amplitude. The resultant motion of the particle is:
| 1. | uniform circular motion |
| 2. | elliptical motion |
| 3. | linear SHM |
| 4. | angular SHM along a circle |
Subtopic: Simple Harmonic Motion |
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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: 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: Spring mass system |
70%
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Two identical simple pendulums are compared, one \((A)\) located on the surface of the earth and the other \((B)\) – at a height \((h)\) above the earth's surface: \(h=\dfrac{R}{1000}.\)
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. \(T_B\Big(1+\dfrac{1}{2000}\Big)=T_A\)
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. \(T_B\Big(1+\dfrac{1}{2000}\Big)=T_A\)
Subtopic: Angular SHM |
60%
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A particle undergoes SHM with an amplitude of \(10\) cm and a time period of \(4\) s. The average velocity of the particle during the course of its motion from its mean position to its extreme position is:
1. \(5\) cm/s
2. \(10\) cm/s
3. at least \(10\) cm/s
4. at most \(10\) cm/s
1. \(5\) cm/s
2. \(10\) cm/s
3. at least \(10\) cm/s
4. at most \(10\) cm/s
Subtopic: Simple Harmonic Motion |
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Two SHMs of the form:
\(x=A+A\text{sin}\omega t\\ y=A-A\text{sin}\omega t\)
are superposed on a particle, along \(x\) and \(y\) directions. The resultant of these motions is:
\(x=A+A\text{sin}\omega t\\ y=A-A\text{sin}\omega t\)
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 |
Subtopic: Simple Harmonic Motion |
54%
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