A uniform circular disc of radius \(50~\text{cm}\) at rest is free to turn about an axis that is perpendicular to its plane and passes through its centre. It is subjected to a torque that produces a constant angular acceleration of \(2.0~\text{rad/s}^2.\) Its net acceleration in \(\text{m/s}^2\) at the end of \(2.0~\text s\) is approximately:
| 1. | \(7\) | 2. | \(6\) |
| 3. | \(3\) | 4. | \(8\) |
What is the minimum velocity with which a body of mass \(m\) must enter a vertical loop of radius \(R\) so that it can complete the loop?
1. \(\sqrt{2 g R}\)
2. \(\sqrt{3 g R}\)
3. \(\sqrt{5 g R}\)
4. \(\sqrt{ g R}\)
| 1. | over a full cycle, the capacitor \(C\) does not consume any energy from the voltage source. |
| 2. | current \(I(t)\) is in phase with voltage \(V(t)\). |
| 3. | current \(I(t)\) leads voltage \(V(t)\) by \(180^{\circ}\). |
| 4. | current \(I(t)\), lags voltage \(V(t)\) by \(90^{\circ}\). |
A uniform rope, of length \(L\) and mass \(m_1,\) hangs vertically from a rigid support. A block of mass \(m_2\) is attached to the free end of the rope. A transverse pulse of wavelength \(\lambda_1\) is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is \(\lambda_2.\) The ratio \(\frac{\lambda_2}{\lambda_1}\) is:
| 1. | \(\sqrt{\dfrac{m_1+m_2}{m_2}}\) | 2. | \(\sqrt{\dfrac{m_2}{m_1}}\) |
| 3. | \(\sqrt{\dfrac{m_1+m_2}{m_1}}\) | 4. | \(\sqrt{\dfrac{m_1}{m_2}}\) |
| 1. | \(0.67~\text{W}\) | 2. | \(0.76~\text{W}\) |
| 3. | \(0.89~\text{W}\) | 4. | \(0.51~\text{W}\) |
| 1. | \( \sqrt{\left(\frac{{E}}{2 {m}}\right)}\) | 2. | \({c}\sqrt{(2 {mE})}\) |
| 3. | \( \frac{1}{{c}}\sqrt{\left(\frac{2 m}{E}\right)}\) | 4. | \(\frac{1}{{c}}\sqrt{\left(\frac{{E}}{2 {m}}\right)}\) |
| 1. | \(\dfrac{1}{\sqrt{m}}\) | 2. | \(\dfrac{1}{m^{2}}\) |
| 3. | \(m\) | 4. | \(\dfrac{1}{m}\) |
| 1. | \(0.15\) m/s2 | 2. | \(0.18\) m/s2 |
| 3. | \(0.2\) m/s2 | 4. | \(0.1\) m/s2 |
| 1. | \(45^{0},~\sqrt{2}\) | 2. | \(30^{0},~\sqrt{2}\) |
| 3. | \(30^{0},~\frac{1}{\sqrt{2}}\) | 4. | \(45^{0},~\frac{1}{\sqrt{2}}\) |