Rotational Motion Question 44
Question: 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]
Options:
A) the velocity of point A is $ 2v _{cm} $ and velocity of point B is zero
B) the velocity of point A is zero and velocity of points is $ 2v _{cm} $
C) the velocity of point A is $ 2v _{cm} $ velocity of point B is $ -v _{cm} $
D) the velocities of both A and B w are $ v _{cm} $
Show Answer
Answer:
Correct Answer: A
Solution:
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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 ) $ $ =2v _{cm} $
Velocity of point B is,
Thus, the velocity of point A is $ 2v _{cm} $ and velocity of point B is zero.
