Q. No.1. \(2 \pi \sqrt{\frac{l}{g} } \)
2. \(2 \pi \sqrt{\frac{g}{l}} \)
3 \(\frac{1}{2} \pi \sqrt{\frac{l}{g}}\)
4. \(\frac{1}{2 \pi} \sqrt{\frac{g}{l}}\)
Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance (\(R/2\)) from the earth's center, where '\(R\)' is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period :
1. \(\frac{2 \pi R}{g} \)
2. \(\frac{\mathrm{g}}{2 \pi \mathrm{R}} \)
3. \(\frac{1}{2 \pi} \sqrt{\frac{g}{R}} \)
4. \(2 \pi \sqrt{\frac{R}{g}} \)
1. \(\sqrt{3}\text{ m}\)
2. \(2\sqrt{3}\text { m}\)
3. \(\frac{\sqrt{3}}{2} \text{ m}\)
4. \(\frac{1}{\sqrt{2}}\text{ m}\)
When two displacements are represented by \(y_1 = a \text{sin}(\omega t)\) and \(y_2 = b\text{cos}(\omega t)\) are superimposed, then the motion is:
| 1. | not simple harmonic. |
| 2. | simple harmonic with amplitude \(\dfrac{a}{b}\). |
| 3. | simple harmonic with amplitude \(\sqrt{a^2+b^{2}}.\) |
| 4. | simple harmonic with amplitude \(\dfrac{a+b}{2}\). |
A particle is performing SHM with amplitude \(A\) and angular velocity \(\omega.\) The ratio of the magnitude of maximum velocity to maximum acceleration is:
1. \(\omega\)
2. \(\dfrac{1}{\omega }\)
3. \(\omega^{2} \)
4. \(A\omega\)
| 1. | \(\pi\) | 2. | \(\pi/2\) |
| 3. | \(2\pi\) | 4. | \(\pi/4\) |
1. \(A~ \text{sin}(\omega t)\)
2. \(B ~\text{cos}(\omega t)\)
3. \(A~ \text{sin}(\omega t)+B ~\text{cos}(\omega t)\)
4. \(A e^{\omega t}+B e^{-\omega t}\)
1. \(\mathit{\pi}\)
2. \(\dfrac{\mathit{\pi}}{2}\)
3. \(\dfrac{\mathit{\pi}}{3}\)
4. \(\dfrac{\mathit{\pi}}{4}\)
The angular velocities of three bodies in simple harmonic motion are with their respective amplitudes as . If all the three bodies have same mass and maximum velocity, then
1.
2.
3.
4.
| 1. | \(1\) s-1 | 2. | \(2\) s-1 |
| 3. | \(\pi\) s-1 | 4. | \(2 \pi\) s-1 |
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