1. Use the condition for maximum speed on a level curved road

For a car moving on a level circular road, friction provides the required centripetal force.

So at the maximum speed without skidding,

$\frac{mv^2}{r} = \mu mg$

Cancelling $m$,

$\frac{v^2}{r} = \mu g$

Hence,

$v = \sqrt{\mu g r}$

This shows that for the same coefficient of friction $\mu$,

$v \propto \sqrt{r}$

2. Relate the two cases

Given:

• Initial radius: $r_1 = 75\,\text{m}$
• Initial maximum speed: $v_1 = 30\,\text{m/s}$
• New radius: $r_2 = 48\,\text{m}$

Using

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

So,

$v_2 = v_1 \sqrt{\frac{r_2}{r_1}} = 30\sqrt{\frac{48}{75}}$

3. Simplify the fraction

$\frac{48}{75} = \frac{16}{25}$

Therefore,

$v_2 = 30\sqrt{\frac{16}{25}} = 30 \cdot \frac{4}{5} = 24\,\text{m/s}$

4. Final Answer

$\boxed{24}$

So the maximum allowed speed is 24 m/s.