Question

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

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

Answer 1

The correct option is A $1:1$

Given that both the cars complete one circle in the same time $t$
We know that angular speed $\omega =\frac{2\pi }{t}\text{rad/s}$

Therefore, the ratio of angular speed of the first car to that of the second car is
$\frac{{\omega }_1}{{\omega }_2}=\frac{\frac{2\pi }{t}}{\frac{2\pi }{t}}=\frac{1}{1}$