Two particles A and B are moving in uniform circular motion in concentric cirdes of radius r

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3-2.Motion in Plane

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Two particles $A$ and $B$ are moving in uniform circular motion in concentric cirdes 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$\mathrm{r}_{\mathrm{A}}: \mathrm{r}_{\mathrm{B}}$

B${v}_{{A}}: {v}_{{B}}$

C$\mathrm{r}_{\mathrm{B}}: \mathrm{r}_{\mathrm{A}}$

D$1: 1$

(NEET-2019)

Solution

$\mathrm{T}_{\mathrm{A}}=\mathrm{T}_{\mathrm{B}}$
$\Rightarrow \frac{2 \pi}{\omega_{A}}=\frac{2 \pi}{\omega_{B}}$
$\Rightarrow \frac{\omega_{A}}{\omega_{B}}=1: 1$

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Solution

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