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Q. No.A particle of mass \(m\) moves in the XY plane with a velocity \(v\) along the straight line AB. If the angular momentum of the particle with respect to the origin \(O\) is \(L_A\) when it is at \(A\) and \(L_B\) when it is at \(B,\) then:
| 1. | \(L_A>L_B\) |
| 2. | \(L_A=L_B\) |
| 3. | the relationship between \(L_A\) and \(L_B\) depends upon the slope of the line \(AB.\) |
| 4. | \(L_A<L_B\) |
The following are the given statements:
| a. | for a general rotational motion, angular momentum \(L\) and angular velocity \(\omega\) need not be parallel. |
| b. | for a rotational motion about a fixed axis, angular momentum \(L\) and angular velocity are always parallel. |
| c. | for a general translational motion, momentum \(p\) and velocity \(v\) are always parallel. |
| d. | for a general translational motion, acceleration \(a\) and velocity \(v\) are always parallel. |
Choose the correct option:
| 1. | (a), (c) |
| 2. | (b), (c) |
| 3. | (c), (d) |
| 4. | (a), (b), (c) |
1. \(\omega_0\)
2. \(2\omega_0\)
3. \(\frac32\omega_0\)
4. \(\frac52\omega_0\)
A uniform rod of mass \(m\) and length \(L\) is struck at both ends by two particles of masses m, each moving with identical speeds \(u,\) but in opposite directions, perpendicular to its length. The particles stick to the rod after colliding with it. The system rotates with an angular speed:
1. \(\frac{u}{L}\)
2. \(\frac{2u}{L}\)
3. \(\frac{12u}{7L}\)
4. \(\frac{6u}{L}\)
If there is no external force acting on a nonrigid body which of the following quantities must remain constant?
| a. | angular momentum |
| b. | linear momentum |
| c. | kinetic energy |
| d. | moment of inertia |
Choose the correct option:
| 1. | (a) and (b) |
| 2. | (b) and (c) |
| 3. | (c) and (d) |
| 4. | (a) and (d) |
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