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

# Two particles A and B are moving in uniform circular motion in concentric circles of radii rA and rB with speed ${\mathrm{\nu }}_{\mathrm{A}}$ and ${\mathrm{\nu }}_{\mathrm{B}}$ respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be

1. A

rB : rA

2. B

1 : 1

3. C

rA : rB

4. D

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

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### Solution:

$\begin{array}{l}{\mathrm{T}}_{\mathrm{A}}={\mathrm{T}}_{\mathrm{B}}=\mathrm{T}⇒{\mathrm{\omega }}_{\mathrm{A}}=\frac{2\mathrm{\pi }}{{\mathrm{T}}_{\mathrm{A}}}⇒{\mathrm{\omega }}_{\mathrm{B}}=\frac{2\mathrm{\pi }}{{\mathrm{T}}_{\mathrm{B}}}\\ \frac{{\mathrm{\omega }}_{\mathrm{A}}}{{\mathrm{\omega }}_{\mathrm{B}}}=\frac{{\mathrm{T}}_{\mathrm{B}}}{{\mathrm{T}}_{\mathrm{A}}}=\frac{\mathrm{T}}{\mathrm{T}}=1\end{array}$

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