A solid cylinder is performing pure rolling motion on a moving platform as shown. Which of the relation between, $v_{0}, ω, R$ and v is correct?

v_{0} = R ω

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v = v_{0} + R ω

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v = v_{0} - R ω

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v = v_{0}

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Solution

The correct option is C $v = v_{0} - R ω$
This is a direct question based on concept of pure rolling. For no slipping relative velocity of point of contact has to be zero. Here velocity of the bottom-most point on cylinder is $v_{0} - R ω$ , and velocity of platform is v. So, from definition of pure rolling, $(v_{0} - R ω) - v = 0 \Rightarrow v = v_{0} - R ω$

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