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Time Period

Two particles...

Question

Two particles $A$ and $B$ are moving in a uniform circular motion in concentric circles of radius $r_{A}$ and $r_{B}$ with speed $v_{A}$ and $v_{B}$ respectively. The time period of rotation is the same. The ratio of angular speed of A to that of B will be

A

r_{A} : r_{B}

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B

v_{A} : v_{B}

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C

r_{B} : r_{A}

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D

1 : 1

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Solution

The correct option is D $1 : 1$
$T_{A} = T_{B} \Rightarrow \frac{2 π}{ω_{A}} = \frac{2 π}{ω_{B}} \Rightarrow \frac{ω_{A}}{ω_{B}} = 1 : 1$

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