Question

A car moves around a curved road of radius R1 at constant speed v without sliding.If we double the car's speed,what is the least radius that would now keep the car from sliding? a)2R1 B)4R1 c)6R1 d)R1

Answer 1

We know that

Centripetal force = mv^2 / r

Since we need a force to counter balance this (in case of car, it's friction)

Let M be mass of car

Friction = Mv^2/ R1 ..........(i)

Now we double the speed, but Max friction remains same

let x be new radius

so Friction = M (2v)^2 / x

Friction = 4 Mv^2/x ............(ii)

from (i) and (ii)

4Mv^2/x = Mv^2/R1

Solve this you get x = 4R1

that's your answer