Question

Two particles X and Y are moving in uniform circular motion in concentric circles of radii rₓ and rᵧ with speed υₓ and υᵧ respectively. Their time period of rotation is the same. The ratio of angular speed of X to that of Y will be :
(1) rₓ : rᵧ
(2) υₓ : υᵧ
(3) rᵧ : rₓ
(4) 1 : 1

Answer 1

The ratio of angular speed of X to that of Y will be 1:1

Step by step explanation:

From the given.

Two particles X and Y.

Radii of "X" particle = $r_{x}$

Radii of "Y" particle = $r_{y}$

The time period of rotation of is same X and Y particles.

$T_{x}=T_{y}=T$

Angular speed of "x" particle:

                 $\bold{\omega _{x}=\frac{2\pi }{T_{x}}}$...............................(1)

Angular speed of "y" particle:

                  $\bold{\omega _{y}=\frac{2\pi }{T_{y}}}$................................(2)

The ratio of "x" and "y" particles will be

                   $\frac{\omega _{x}}{\omega _{y}}=\frac{T_{y}}{T_{x}}$

                       $\Rightarrow \frac{T}{T}=1$

Therefore, The ratio of angular speed of X to that of Y will be 1:1

Hence, correct answer - 4