What is the maximum speed with which a vehicle can take the turn on a curved frictionless smooth road of width 4 m , without skidding, if the radius of the circular curve of the road is 9 m and the outer edge of the road above the inner edge is 40 cm high? [given g= 1 0 ms ⁻² ]

Step-by-step solution

For a vehicle moving on a banked road without skidding, the required centripetal force is provided by the horizontal component of the normal reaction. The angle of banking is given by = h b , where h is the height of the outer edge above the inner edge and b is the width of the road. Given h = 40 cm = 0.4 m and b = 4 m , we have = 0.4 4 = 0.1 . The maximum speed v for a banked road without friction is given by v = rg , where r is the radius of the curve and g is the acceleration due to gravity. Substituting the giv