Question

Two cars $c_1$ and $c_2$ are going around in concentric circles of radii $r_1$ and $r_2$. They complete the circular paths in the same time. Then, the ratio of speed of $c_1$ to speed of $c_2$ is

• A. $\frac{r_2}{r_1}$
• B. $\frac{r_1}{r_2}$
• C. $1$
• D. None of these

Answer 1

The correct option is B $\frac{r_1}{r_2}$

Given the time periods are same.
i.e $T_1=T_2$
$\Rightarrow \frac{2\pi }{{\omega }_1}=\frac{2\pi }{{\omega }_2}$
$\Rightarrow {\omega }_1={\omega }_2$
Therefore, ratio of speeds $\frac{v_1}{v_2}=\frac{{\omega }_1{r}_1}{{\omega }_2{r}_2}=\frac{r_1}{r_2}$