Question

A bend in a level road has a radius of 10m. Calculate the maximum speed which a car turning this bend may have without skidding. ($\mu = 0.81$)
A. 6m/s
B. 3m/s
C. 4m/s
D. 9m/s

Answer 1

Given question refers to the phenomena of banking of roads. In banking of roads, edges are raised for the curved roads above the inner edge to provide the required centripetal force to the vehicle so that they do not skid and take a safe turn. Here centripetal force is equal to the frictional force. So equate these forces to find the value of maximum speed.

Complete step by step answer:
We are given that a bend in a level road has a radius of 10m.
We have to calculate the maximum speed which a car turning this bend may have without skidding.
So for the car to have maximum speed and not skid, centripetal force acting on it must be equal to frictional force it is exerting.
Centripetal force can be calculated using $\dfrac{{m{v^2}}}{r}$, where ms is the mass of the car, v is the speed and r is the radius of the bend.
Frictional force can be calculated using $\mu mg$, where g is the acceleration due to gravity and $\mu$ is the coefficient of friction.
Therefore,
$\dfrac{{mv_{\max }^2}}{r} = \mu mg \\\ \Rightarrow v_{\max }^2 = \mu gr \\\ \therefore {v_{\max }} = \sqrt {\mu gr} \\\ r = 10m,g = 10m/{s^2},\mu = 0.81 \\\ \Rightarrow{v_{\max }} = \sqrt {10 \times 0.81 \times 10} = \sqrt {81} \\\ \therefore {v_{\max }} = 9m/s \\\$
Therefore, the correct option is Option D, 9m/s.

Note: Do not confuse centripetal force with centrifugal force. Centripetal force is the force that puts an object in a curved or circular path whereas centrifugal force is the apparent force felt by an object moving in a curved path. Centripetal acts inwards and centrifugal act outwards.