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It is because it moves at a uniform speed at the same period of time.
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A body in uniform circular motion has a uniform velocity of motion,i.e;equal distance is covered in equal amounts of time .
A particle under UCM covers a constant distance in completing circular trajectory in one revolution, which is equal to the perimeter of the circle.
Further the particle covers the perimeter with constant speed. It means that the particle travels the circular trajectory in a constant time given by its time period as :
Hope i helped u:)
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