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Q. No.An elastic ball rebounds vertically to a height \(h\) above the ground, the period of its motion will be:
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.
\(\begin{aligned} 2\large{\sqrt\frac{h}{g}} & \\ \end{aligned}\)
Subtopic: Types of Motion |
Level 3: 35%-60%
Hints
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. | \(2\pi\sqrt{\dfrac{l}{g}}+2\pi\sqrt{\dfrac{m}{k}}\) | 2. | \(\pi\sqrt{\dfrac{l}{g}}+\pi\sqrt{\dfrac{m}{k}}\) |
| 3. | \(\sqrt{\dfrac{g}{l}}+\sqrt{\dfrac{k}{m}}\) | 4. | \(\dfrac{1}{2\pi}\sqrt{\dfrac{g}{l}}+\dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}}\) |
Subtopic: Spring mass system |
52%
Level 3: 35%-60%
Hints
A small block of mass \(m\) slides a distance \(L\) down a smooth incline and rebounds elastically back up. The period of the motion is: (using standard symbols where necessary)
| 1. | \(\sqrt{\dfrac{4L\sin\theta}{g}} \) | 2. | \(\sqrt{\dfrac{8L\sin\theta}{g}} \) |
| 3. | \(\sqrt{\dfrac{8L}{g\sin\theta}} \) | 4. | \(\sqrt{\dfrac{4L}{g\sin\theta}} \) |
Subtopic: Linear SHM |
Level 3: 35%-60%
Hints
Consider a particle undergoing uniform circular motion, with angular speed \(\omega.\) The projection of its motion on any straight line in its plane is:
| 1. | periodic but not SHM |
| 2. | SHM with angular frequency \(\omega\) |
| 3. | SHM but angular frequency \(2\omega\) |
| 4. | neither SHM nor periodic |
Subtopic: Phasor Diagram |
52%
Level 3: 35%-60%
Hints
A physical pendulum consists of a uniform rod \(AB\) of mass \(m\) and length \(L,\) suspended from one end \(A\) – so as to rotate freely under gravity. If it is displaced slightly from its mean position, it executes SHM. Let the maximum kinetic energy of the rod be \(E_0.\)
If the time period of a simple pendulum of the same length is \(T_0,\) then the time period of this pendulum is:
If the time period of a simple pendulum of the same length is \(T_0,\) then the time period of this pendulum is:
| 1. | \(\sqrt{\dfrac{2}{3}} T_0\) | 2. | \(\sqrt{\dfrac{1}{12}} T_0\) |
| 3. | \(\sqrt{\dfrac{3}{2}} T_0\) | 4. | \(T_0\) |
Subtopic: Angular SHM |
53%
Level 3: 35%-60%
Hints
The graph represents the variation of the position of a particle \((x)\) as a function of time \((t);\) the variation being sinusoidal.
The amplitude of the motion of the particle is:
1. \(6~\text{cm}\)
2. \(3~\text{cm}\)
3. \(1.5~\text{cm}\)
4. \(12~\text{cm}\)
The amplitude of the motion of the particle is:
1. \(6~\text{cm}\)
2. \(3~\text{cm}\)
3. \(1.5~\text{cm}\)
4. \(12~\text{cm}\)
Subtopic: Simple Harmonic Motion |
51%
Level 3: 35%-60%
Hints
Which, of the following, represents the displacement in simple harmonic motion?
| (A) | \(x=A\sin^2\omega t\) |
| (B) | \(x=A\sin\omega t+B\cos2\omega t\) |
| (C) | \(x=A\sin^2\omega t+B\cos2\omega t\) |
| 1. | A only | 2. | A and B |
| 3. | A and C | 4. | A, B and C |
Subtopic: Types of Motion |
Level 4: Below 35%
Hints
Two particles undergo SHM along the same straight line, moving with the same frequency and amplitude but with a phase difference of \(60^\circ\) between each other. If they have a maximum speed of \(v_0,\) the maximum relative velocity between them will be:
| 1. | \(v_0\) | 2. | \(2v_0\) |
| 3. | \({\dfrac{\sqrt3}{2}}v_0\) | 4. | \(\sqrt3v_0 \) |
Subtopic: Phasor Diagram |
Level 3: 35%-60%
Hints
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: Spring mass system |
Level 3: 35%-60%
Hints
Two identical masses are connected by a spring of spring constant \(k,\) and the individual masses are observed to undergo SHM with their centre of mass remaining at rest. The amplitude of oscillation of one of the masses is \(A.\) The total energy of oscillation is:
1. \({\Large\frac{1}{2}}kA^2\)
2. \(kA^2\)
3. \(2kA^2\)
4. \(4kA^2\)
1. \({\Large\frac{1}{2}}kA^2\)
2. \(kA^2\)
3. \(2kA^2\)
4. \(4kA^2\)
Subtopic: Energy of SHM |
Level 4: Below 35%
Hints
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