Question

Two cars A and B take same time to go round two concentric circular traks of radii r1 and r2 resp., If r2 = 4r1 , the ratio of angular speed of car A to that of car B is ?

Answer 1

Answer: 1 : 1

Step-by-Step-Explanation:

Given: Time Taken is same

We Know That ω=2π/T

Given That T is Constant So ω = Constant.

Both Their Angular Velocities are same.

Ratio of Their Angular Velocities = 1 : 1

Answer 2

The ratio of angular speed of car A to that of car B is 1:1.

• Angular velocity is the rate of change of angular displacement.
• It is given by

                         ω = $\alpha/t$

                         ω = angular velocity

                          $\alpha =$angular displacement

                          t = time taken

Problem:

• Given

                         $t_{1}=t_{2}=t$

                         $r_{2}=4r_{1}$

• When cars go round the circle, then their angular displacements will be

                          $\alpha_{1}=\alpha _{2}=2\pi$

                          $w_{1}:w_{2}=\frac{2\pi}{t}:\frac{2\pi}{t}\\w_{1}:w_{2}=1:1$