Calculate the maximum speed with which a vehicle can travel on a banked circular road without skidding. A cyclist at a 18 km/h on a level road takes a sharp turn of radius 3 m without reducing the speed. The coefficient of static friction between the tyres and the road is 1. Will cyclist slip while taking the turn?

Explanation

Here, v = 18 km/h = 5 m/s, r = 3 m and `mu_(s)` = 1
only frictional force can provide the centripetal force on an unbanked road.
The condition for which the cyclist will not slip is
`(mv^(2))/(r ) le F_(s)`
or, `" " (mv^(2))/(r ) le mu_(3) mg " " or, v^(2) le mu_(s) rg`
Here, `v^(2) = 25`
and `" "mu_(s) rg = 1 xx 3 xx 10 = 30`
Since, `25 lt 30` , therefore it satisfies the condition `v^(2) le mu_(s)`rg.
Hence, the cyclist will not slip while taking the turn.