Question

two bodies are moving on two different circular tracks with the same speed . if the ratio of radii of circular tracks is 2:1 then their respective angular speeds are in ratio of
a. 1:1
b. 2:1
c. 1:2
d. 1:4​

Answer 1

Given:

Two bodies are moving on two different circular tracks with the same speed . Ratio of radii of the circular tracks is 2 : 1

To find:

Ratio of angular speed ?

Calculation:

Let constant of proportionality be "x", so the radii of the tracks will be 2x and x:

Now, let the linear speed be v :

Let angular speed be denoted as $\omega$:

For the 1st object:

$\therefore \omega1 = \dfrac{v}{r1} = \dfrac{v}{2x}$

For the 2nd object:

$\therefore \omega2 = \dfrac{v}{r2} = \dfrac{v}{x}$

So, required ratio:

$\therefore \: \omega1 : \omega2 = \dfrac{v}{2x} : \dfrac{v}{x}$

$\implies\: \omega1 : \omega2 = \dfrac{1}{2} : 1$

$\implies\: \omega1 : \omega2 = 1 : 2$

So, final answer is:

$\boxed{ \bold{\: \omega1 : \omega2 = 1 : 2}}$