Question

Two racing cars of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$ respectivey. Their speeds are such that each makes a complete circle in the same duration of time $t$. The ratio of the angular speed of the first to the second car is

• A. $m_1:m_2$
• B. $r_1:r_2$
• C. $1:1$
• D. $m_1{r}_1:m_2{r}_2$

Answer 1

Answer: (C)

$1:1$

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'

$\text{Angular speed}=\omega =\frac{\text{angle subtended by the car for one revolution}\left(2\pi \right)}{\text{Time Taken}\left(t\right)}$

$\text{Angular speed of first car},={\omega }_1=\frac{2\pi }{t}$

$\text{Angular speed of second car},={\omega }_2=\frac{2\pi }{t}$

$\text{The ratio of angular speed of first car to that of second}=\frac{{\omega }_1}{{\omega }_2}=1:1$