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Instantaneous Velocity

A disc is rol...

Question

A disc is rolling without slipping with some angular velocity. P and Q are two points equidistant from the centre C. The correct relation among the following is:

v_{Q} > v_{C} > v_{P}

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v_{P} > v_{C} > v_{Q}

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v_{P} = v_{C}, v_{Q} = \frac{v_{C}}{2}

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v_{P} < v_{C} > v_{Q}

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Solution

The correct option is D $v_{P} > v_{C} > v_{Q}$
Since the C in center to its velocity will be $V_{c m}$
now point P will have velocity resultant of $V_{c m}$ and $ω r$ and angle between them is less than $90^{o}$
so Resultant velocity of $P > V_{c m}$
now point Q will have velocity resultant of $V_{c m} a n d ω r$ and angle between them is greater than $90^{o}$
so Resultant velocity of $Q > V_{c m}$

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