Short Answer

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01

Expression for the linear speed and the circumference of the circle: 

02

Determine the ratio of the circumference to the diameter:

As the radius stays the same in the inertial frame of reference to another frame of reference, the radius of a circular field does not expand or contract. For considering the circumference, there should be Lorentz-contracted to a smaller value than at rest by a Lorentz factor y. Hence,

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