| A wheel of bicycle is rolling without slipping on a level road. The velocity of the centre of mass is \[{{v}_{cm}};\] then true statement is: [AIPMT 2001] |
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A) the velocity of point A is \[2\,{{v}_{cm}}\] and velocity of point B is zero
B) the velocity of point A is zero and velocity of points is \[2\,{{v}_{cm}}\]
C) the velocity of point A is \[2\,{{v}_{cm}}\] velocity of point B is \[-\,\,{{v}_{cm}}\]
D) the velocities of both A and B w are \[{{v}_{cm}}\]
Correct Answer: A
Solution :
| Key Idea: For a body rolling without slipping, the velocity of any point P on the body is \[{{\vec{v}}_{p}}={{\vec{v}}_{cm}}+{{\vec{v}}_{p,\,cm}}\] where \[{{\vec{v}}_{p,\,cm}}=R\omega \] in direction perpendicular to line joining centre and point P. |
| Velocity of point A is, |
| \[{{v}_{A}}={{v}_{cm}}+R\omega \] |
| \[={{v}_{cm}}+{{v}_{cm}}\] \[(\because \,{{v}_{cm}}=R\omega )\] |
| \[=2{{v}_{cm}}\] |
| Velocity of point B is, |
| Thus, the velocity of point A is \[2\,{{v}_{cm}}\] and velocity of point B is zero. |
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