Question

A van is moving with a speed of 108 km/hr on a level road where the coefficient of friction between the tyres and the road is 0.5. For the safe driving of the van, the minimum radius of curvature of the road shall be (Acceleration due to gravity, g=10 m/s2)

• A. 180 m
• B. 120 m
• C. 80 m
• D. 40 m

Answer 1

Answer: (A)

180 m

Answer 2

The centripetal force required to keep the van moving in a curved path is given by:
Fc = $\frac {mv^2}{r}$
The maximum frictional force that can be provided by the tires is given by:
Ffriction = μmg
For safe driving, the maximum centripetal force must be less than or equal to the maximum frictional force. Therefore, we can equate the two expressions:
$\frac {mv^2}{r}$ = μmg
$\frac {v^2}{r}$ = μg
r = $\frac {v^2}{μg}$
Now we can substitute the given values:
v = 108 km/hr
v = = $\frac {108,000\ m}{3600\ s}$
v = 30 m/s
μ = 0.5
g = 10 m/s2
r = $\frac {(30 m/s)^2}{0.5 \times 10 \ m/s^2}$
r = $\frac {900}{5}$ m
r = 180 m
Therefore, the minimum radius of curvature of the road for safe driving is 180 meters.
So, the correct option is (A) 180 m.