Q. No.A particle of mass \(m\) is released from rest and follows a parabolic path as shown. Assuming that the displacement of the mass from the origin is small, which graph correctly depicts the position of the particle as a function of time?
1.
2.
3.
4.
A mass of \(2.0\) kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes a simple harmonic motion. The spring constant is \(200\) N/m. What should be the minimum amplitude of the motion, so that the mass gets detached from the pan?
(Take \(g=10\) m/s2)
| 1. | \(8.0\) cm |
| 2. | \(10.0\) cm |
| 3. | any value less than \(12.0\) cm |
| 4. | \(4.0\) cm |
The radius of the circle, the period of revolution, initial position and direction of revolution are indicated in the figure.
The \(y\)-projection of the radius vector of rotating particle \(P\) will be:
| 1. | \(y(t)=3 \cos \left(\dfrac{\pi \mathrm{t}}{2}\right)\), where \(y\) in m |
| 2. | \(y(t)=-3 \cos 2 \pi t\) , where \(y\) in m |
| 3. | \(y(t)=4 \sin \left(\dfrac{\pi t}{2}\right)\), where \(y\) in m |
| 4. | \(y(t)=3 \cos \left(\dfrac{3 \pi \mathrm{t}}{2}\right) \), where \(y\) in m |
| 1. | \(1:9\) | 2. | \(1:11\) |
| 3. | \(1:14\) | 4. | \(1:6\) |
When a mass \(m\) is connected individually to two springs \(S_1\) and \(S_2,\) the oscillation frequencies are \(\nu_1\) and \(\nu_2.\) If the same mass is attached to the two springs as shown in the figure, the oscillation frequency would be:
| 1. | \(v_2+v_2\) | 2. | \(\sqrt{v_1^2+v_2^2}\) |
| 3. | \(\left(\dfrac{1}{v_1}+\dfrac{1}{v_1}\right)^{-1}\) | 4. | \(\sqrt{v_1^2-v_2^2}\) |
1. \(\frac{\pi}{6}\)
2. \(0\)
3. \(\frac{2\pi}{3}\)
4. \(\pi\)
Two pendulums suspended from the same point have lengths of \(2\) m and \(0.5\) m. If they are displaced slightly and released, then they will be in the same phase when the small pendulum has completed:
1. \(2\) oscillations
2. \(4\) oscillations
3. \(3\) oscillations
4. \(5\) oscillations
| 1. | \(0.01~\text{Hz}\) | 2. | \(0.02~\text{Hz}\) |
| 3. | \(0.03~\text{Hz}\) | 4. | \(0.04~\text{Hz}\) |
A particle executing simple harmonic motion of amplitude \(5~\text{cm}\) has a maximum speed of \(31.4~\text{cm/s}.\) The frequency of its oscillation will be:
1. \(1~\text{Hz}\)
2. \(3~\text{Hz}\)
3. \(2~\text{Hz}\)
4. \(4~\text{Hz}\)
The frequency of a simple pendulum in a free-falling lift will be:
1. zero
2. infinite
3. can't say
4. finite
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