Question

Two racing cars of masses $ m_{1} $ and $ m_{2} $ are moving in a circles of radii $ r_{1} $ and $ r_{2} $ respectively. Their speeds are such that each makes a complete round of circle in the same internal of time. The ratio of their angular speeds are :

• A. $ m_{1}m_{2} : r_{1}r_{2} $
• B. $1 : 1$
• C. $ r_{1} : r_{2} $
• D. $ m_{2} : m_{1} $

Answer 1

Answer: (B)

Angular velocity is the rate of change of angular displacement with time.
Given that both the cars complete one circle in the same time '$t$'
Angular speed $=\omega=\frac{\text { angle subtended by the car for one revolution }(2 \pi)}{\text { Time Taken( }(t)}$
Angular speed of first car, $=\omega_{1}=\frac{2 \pi}{t}$
Angular speed of second car, $=\omega_{2}=\frac{2 \pi}{t}$
The ratio of angular speed of first car to that of second $=\frac{\omega_{1}}{\omega_{2}}=1: 1$