My Notes
A small mass attached to a string rotates on a frictionless table top as shown. If the tension on the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of \(2,\) the kinetic energy of the mass will
| 1. | Increase by a factor of \(4\) |
| 2. | Decrease by a factor of \(2\) |
| 3. | Remain constant |
| 4. | Increase by a factor of \(2\) |
A solid sphere is rotating about a diameter at an angular velocity \(w.\) If it cools so that its radius reduces to\(\frac1n\) of its original value, its angular velocity becomes
1. \(\frac wn\)
2. \(\frac{w}{{n}^2}\)
3. \(nw\)
4. \(n^2w\)
A horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its centre. At some instant of time a viscous fluid of mass 'm' is dropped at the centre and is allowed to spread out and finally fall. The angular velocity during this period
1. Decreases continuously
2. Decreases initially and increases again
3. Remains unaltered
4. Increases continuously
In an orbital motion, the angular momentum vector is
1. Along the radius vector
2. Parallel to the linear momentum
3. In the orbital plane
4. Perpendicular to the orbital plane
A particle of mass \(m\) moves with a constant velocity along \(3\) different paths, \(DE, OA\) and \(BC\). Which of the following statements is not correct about its angular momentum about point \(O\)?
| 1. | It is zero when it is at \(A\) and moving along \(OA\). |
| 2. | The same at all points along the line \(DE\). |
| 3. | Of the same magnitude but oppositely directed at \(B\) and \(D\). |
| 4. | Increases as it moves along the line \(BC\). |
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