Two particles A and B are moving in uniform circular motion in concentric circles of radii and with speed and respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be [2019]

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Solution

Q.
Two particles A and B are moving in uniform circular motion in concentric circles of radii $r_{A}$ and $r_{B}$ with speed $v_{A}$ and $v_{B}$ respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be [2019]

1 $1 : 1$

2 $r_{A} : r_{B}$

3 $v_{A} : v_{B}$

4 $r_{B} : r_{A}$

Ans.
(1)

Time period, $T = \frac{2 π}{ω}$

As $T_{A} = T_{B} .$ So, $\frac{2 π}{ω_{A}} = \frac{2 π}{ω_{B}}$ or $ω_{A} : ω_{B} = 1 : 1$

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