Question

A curve on a level road has a radius $75m$. The maximum speed of a car turning on this curved road can be $30m/s$ without skidding. If radius of curved road is changed to $48m$ and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed should be $m/s$

Answer 1

Condition for no skidding,
$f_{s_{max}}=\frac{m{v}^2}{r}$

Also static friction, $f_{s_{max}}=\mu mg$

$\Rightarrow \mu mg=\frac{m{v}^2}{r}$

$\Rightarrow v=\sqrt{\mu gr}$

Since coefficient of friction remains same,

$\Rightarrow \frac{v_1}{v_2}=\sqrt{\frac{r_1}{r_2}}$

$\Rightarrow \frac{30}{v_2}=\sqrt{\frac{75}{48}}=\sqrt{\frac{25}{16}}=\frac{5}{4}$

$\Rightarrow v_2=24m/s$