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A wheel rolls purely between a rough horizontal surface below it and a horizontal plank above it under the action of a horizontal force $F$ applied on the plank. If at any time $\vec{v_{p}}$ and $\vec{v_{c}}$ represent velocity of plank and velocity of centre of mass of wheel and $\vec{a_{p}}$ and $\vec{a_{c}}$ represent acceleration of plank and acceleration of centre of mass of wheel respectively then which of the following is/are correct.

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$|\vec{v_{p}}| = |\vec{v_{c}}|$

$|\vec{v_{p}}| = 2 |\vec{v_{c}}|$

$|\vec{a_{p}}| = 2 |\vec{a_{c}}|$

$|\vec{a_{p}}| = |\vec{a_{c}}|$

answer is A, B.

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Detailed Solution

For pure rolling of wheel $w r t$ horizontal surface below it

$V_{p} = V_{c} + R ω = 2 V_{c}$

$∴ \frac{d v_{p}}{d t} = \frac{2 d v_{c}}{d t}$ ;

$\Rightarrow a_{p} = 2 a_{c}$

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