Question

"Two cyclists cycle along circular track of radius R1 and R2 at uniform rates if both of them take same time to complete one revolution, then there angular speeds are in ratio

Answer 1

Ans is 1: 1 .How much ever the radii is,angular dispacement depend only on angle and also they take the same time.Hence they have equal angular speeds

Answer 2

Answer:

Angular Speeds are in the ratio 1 : 1

Explanation:

[Refer to the attached image]

Given;-

             Rate at which R₁, R₂ cycle = Uniform [indicating that the case is of uniform circular motion]

             Time taken, t= Same for R₁ & R₂

Now;-

We know that, for uniform circular motion;-

           Angular Speed, ω= 2π/ t   [where t= time]

Then;-

                         ω = 2π/ t

                         ω = Constant  [since t is same for both of them]

So, we can say that R₁ = R₂  ______(1)

Now, Let ω₁ and ω₂ be Angular Speed for R₁ and R₂ respectively. Then;-

               ω₁/ ω₂ = R₁/ R₂

               ω₁/ ω₂ = 1 / 1   [from (1)]

Therefore, there angular speeds are in the ratio 1 : 1.

Hope it helps! ;-))