Two cars going round curve with speeds one at 90 km/h and other at 15 km/h. Each car experiences same acceleration. The radii of curves are in the ratio of

The correct option is 36 : 1.

Step-by-Step Explanation:

Let the speed of the first car be $v_1$ and the speed of the second car be $v_2$.
We are given:
$v_1=90\text{km/h}$
$v_2=15\text{km/h}$

Let the radius of the curve for the first car be $r_1$ and for the second car be $r_2$.
When a car goes around a curve of radius $r$ at a speed $v$, it experiences a centripetal acceleration $a$ given by the formula:
$a=\frac{v^2}{r}$

According to the problem, both cars experience the same acceleration ($a_1=a_2=a$). Therefore, we can write:
$\frac{{v_1}^2}{r_1}=\frac{{v_2}^2}{r_2}$

Rearranging the equation to find the ratio of the radii ($r_1:r_2$):
$\frac{r_1}{r_2}={\left(\frac{v_1}{v_2}\right)}^2$

Substitute the given values of speed into the equation:
$\frac{r_1}{r_2}={\left(\frac{90}{15}\right)}^2$

Simplify the fraction inside the parenthesis:
$\frac{90}{15}=6$
Therefore, we have:
$\frac{r_1}{r_2}=6^2=36$

So, the ratio of the radii of the curves is:
$r_1:r_2=36:1$