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A cylinder rolls without slipping over a horizontal plane with constant velocity. The radius of the cylinder is equal to $r$ . The radii of curvature of the trajectory traced out by the point $A$ in figure has the relation

$R_{A} = 4 r$
$R_{B} = \sqrt{2} r$
$R_{A} = r$
$R_{B} = 4 r$

A

R_{B} = \sqrt{2} r

B

R_{A} = 4 r

C

R_{A} = r

D

R_{B} = 4 r

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