Q. No.A frictionless wire \(AB\) is fixed on a sphere of radius \(R\). A very small spherical ball slips on this wire. The time taken by this ball to slip from \(A\) to \(B\) is:
1. \(\frac{2 \sqrt{g R}}{g \cos \theta}\)
2. \(2 \sqrt{g R} . \frac{\cos \theta}{g}\)
3. \(2 \sqrt{\frac{R}{g}}\)
4. \(\frac{g R}{\sqrt{g\cos \theta}}\)
1. \(\frac{2 \sqrt{g R}}{g \cos \theta}\)
2. \(2 \sqrt{g R} . \frac{\cos \theta}{g}\)
3. \(2 \sqrt{\frac{R}{g}}\)
4. \(\frac{g R}{\sqrt{g\cos \theta}}\)
A body is slipping from an inclined plane of height \(h\) and length \(l\). If the angle of inclination is \(\theta\), the time taken by the body to come from the top to the bottom of this inclined plane is:
1. \(\sqrt{\frac{2 h}{g}}\)
2. \(\sqrt{\frac{2 l}{g}}\)
3. \(\frac{1}{\sin \theta} \sqrt{\frac{2 h}{g}}\)
4. \(\sin \theta \sqrt{\frac{2 h}{g}}\)
An airplane is moving with a velocity \(u.\) It drops a packet from a height \(h.\) The time \(t\) taken by the packet to reach the ground will be:
1. \( \sqrt{\frac{2 g}{h}} \)
2. \( \sqrt{\frac{2 u}{g}} \)
3. \( \sqrt{\frac{h}{2 g}} \)
4. \( \sqrt{\frac{2 h}{g}}\)
A body sliding on a smooth inclined plane requires \(4\) seconds to reach the bottom starting from the rest at the top. How much time does it take to cover one-fourth distance starting from the rest at the top?
| 1. | \(1~\text{s}\) | 2. | \(2~\text{s}\) |
| 3. | \(4~\text{s}\) | 4. | \(16~\text{s}\) |
The time taken by a block of wood (initially at rest) to slide down a smooth inclined plane \(9.8~\text{m}\) long (angle of inclination is \(30^{\circ}\)
| 1. | \(\frac{1}{2}~\text{sec} \) | 2. | \(2 ~\text{sec} \) |
| 3. | \(4~ \text{sec} \) | 4. | \(1~\text{sec} \) |
A particle moves with constant angular velocity in a circle. During the motion its:
| 1. | Energy is conserved |
| 2. | Momentum is conserved |
| 3. | Energy and momentum both are conserved |
| 4. | None of the above is conserved |
| 1. | \(6 \hat{i}+2 \hat{j}-3 \hat{k} \) |
| 2. | \(-18 \hat{i}-13 \hat{j}+2 \hat{k} \) |
| 3. | \(4 \hat{i}-13 \hat{j}+6 \hat{k}\) |
| 4. | \(6 \hat{i}-2 \hat{j}+8 \hat{k}\) |
A particle moves with constant speed \(v\) along a circular path of radius \(r\) and completes the circle in time \(T\). The acceleration of the particle is:
1. \(2\pi v / T\)
2. \(2\pi r / T\)
3. \(2\pi r^2 / T\)
4. \(2\pi v^2 / T\)
If the equation for the displacement of a particle moving on a circular path is given by \(\theta = 2t^3 + 0.5\) where \(\theta\) is in radians and \(t\) in seconds, then the angular velocity of the particle after \(2\) sec from its start is:
1. \(8\) rad/sec
2. \(12\) rad/sec
3. \(24\) rad/sec
4. \(36\) rad/sec
The coordinates of a moving particle at any time \(t\) are given by \(x= \alpha t^3\) and \(y = \beta t^3.\) The speed of the particle at a time \(t\) is given by:
| 1. | \(\sqrt{\alpha^{2} + \beta^{2}}\) | 2. | \(3t \sqrt{\alpha^{2} + \beta^{2}}\) |
| 3. | \(3t^{2} \sqrt{\alpha^{2} +\beta^{2}}\) | 4. | \(t^{2} \sqrt{\alpha^{2} +\beta^{2}}\) |
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