A

Step 1: Understand the forces acting on the car while turning. The frictional force provides the necessary centripetal force for the car to turn.
Step 2: The maximum frictional force (F_f) can be calculated using the formula:
F_f = \mu \cdot N
where \mu = 0.4 (coefficient of friction) and N = mg (normal force, which equals the weight of the car).
Given that g = 10 m/s², we have F_f = 0.4 \cdot mg.
Step 3: The centripetal force (F_c) required to keep the car moving in a circle of radius r (30 m) at speed v is given by:
F_c = \frac{mv^2}{r}
Step 4: For the car to turn without skidding, the frictional force must equal the centripetal force:
0.4 \cdot mg = \frac{mv^2}{r}.
Step 5: The mass m can be canceled out from both sides since it appears in both terms:
0.4g = \frac{v^2}{r}.
Step 6: Solving for the maximum speed v:
v^2 = 0.4gr
v = \sqrt{0.4gr}.
Step 7: Substituting g = 10 m/s² and r = 30 m:
v = \sqrt{0.4 \cdot 10 \cdot 30} = \sqrt{120} = 10.95 m/s.
Therefore, the maximum speed at which the car can turn round the curve is approximately 10.95 m/s.