Question

Two cars A and B move along a concentric circular path of radius $rA$ and $rB$ with velocities $VA$ and $VB$ maintaining constant distance, then $\fracVAVB}$ is equal to

• A. $\frac{r_{B}}{r_{A}}$
• B. $\frac{r_{A}}{r_{B}}$
• C. $\frac{r_{A}^{2}}{r_{B}^{2}}$
• D. $\frac{r_{B}^{2}}{r_{A}^{2}}$

Hint:

Two cars A and B move along a concentric circular path of radius $rA$ and $rB$ with velocities $VA$ and $VB$ maintaining constant distance, then $VA/VB$ is equal to

Answer 1

The Correct Option is B

To solve this problem, we need to understand the motion of two cars, A and B, moving along concentric circular paths with radii \( r_A \) and \( r_B \) and velocities \( V_A \) and \( V_B \) respectively.

The key part of the question is that the cars maintain a constant distance, implying that they have the same angular speed. The formula for angular speed \( \omega \) in circular motion is given by:

\(\omega = \frac{V}{r}\)

Since the two cars maintain a constant distance while moving along their respective paths, they should have the same angular speed:

Equating the angular speeds for both cars:

\(\frac{V_A}{r_A} = \frac{V_B}{r_B}\)

We can rearrange this equation to find the ratio of their velocities:

\(\frac{V_A}{V_B} = \frac{r_A}{r_B}\)

Thus, the correct option is:

\(\frac{r_A}{r_B}\)

Let's rule out the incorrect options:

1. \(\frac{r_B}{r_A}\): This would be true if the velocities were proportional inversely, but here they are proportional directly.
2. \(\frac{r_A^2}{r_B^2}\) and \(\frac{r_B^2}{r_A^2}\): These do not match the concept of direct proportionality of velocity with respect to radius.

Conclusion: The ratio of their velocities is \(\frac{V_A}{V_B} = \frac{r_A}{r_B}\).