Q. No.One end of a spring of force constant \(k\) is fixed to a vertical wall and the other to a block of mass \(m\) resting on a smooth horizontal surface. There is another wall at a distance \(x_0\) from the block. The spring is then compressed by \(2x_0\)
1.
\(\frac{1}{6} \pi \sqrt{ \frac{k}{m}}\)
2.
\( \sqrt{\frac{k}{m}}\)
3.
\(\frac{2\pi}{3} \sqrt{ \frac{m}{k}}\)
4.
\(\frac{\pi}{4} \sqrt{ \frac{k}{m}}\)
1. \(\frac{1}{2}\)
2. \(\frac{1}{4}\)
3. \(1\)
4. \(\frac{1}{8}\)
A block is connected to a relaxed spring and kept on a smooth floor. The block is given a velocity towards the right. Just after this:
| 1. | the speed of block starts decreasing but acceleration starts increasing. |
| 2. | the speed of the block as well as its acceleration starts decreasing. |
| 3. | the speed of the block starts increasing but its acceleration starts decreasing. |
| 4. | the speed of the block as well as acceleration start increasing. |
A mass m is suspended from two springs of spring constant as shown in the figure below. The time period of vertical oscillations of the mass will be
1.
2.
3.
4.
| 1. | Spring constant | 2. | Angular frequency |
| 3. | (Angular frequency)2 | 4. | Restoring force |
1. \(y = 0.5\sin(5\pi t)\)
2. \(y = 0.5\sin(4\pi t)\)
3. \(y = 0.5\sin(2.5\pi t)\)
4. \(y = 0.5\cos(5\pi t)\)
| 1. | \(A_1 \omega_1=A_2 \omega_2=A_3 \omega_3\) |
| 2. | \(A_1 \omega_1^2=A_2 \omega_2^2=A_3 \omega_3^2\) |
| 3. | \(A_1^2 \omega_1=A_2^2 \omega_2=A_3^2 \omega_3\) |
| 4. | \(A_1^2 \omega_1^2=A_2^2 \omega_2^2=A^2\) |
1. \(\propto x\)
2. \(\propto x^2\)
3. Independent of \(x\)
4. \(\propto x^{\frac{1}{2}}\)
A body is executing simple harmonic motion. At a displacement \(x,\) its potential energy is \(E_1\) and at a displacement \(y\), its potential energy is \(E_2\). The potential energy \(E\) at displacement \(x+y\) will be?
1. \(E = \sqrt{E_1}+\sqrt{E_2}\)
2. \(\sqrt{E} = \sqrt{E_1}+\sqrt{E_2}\)
3. \(E =E_1 +E_2\)
4. None of the above
| 1. | \(2 \pi \over K\) | 2. | \(2 \pi K\) |
| 3. | \(2 \pi \over \sqrt{K}\) | 4. | \(2 \pi \sqrt{K}\) |
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