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Question

A car has to move on a level turn of radius 45 m. If the coefficient of static friction between the tyre and the road is 2.0, find the maximum speed the car can take without skidding.

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Solution

The correct option is **B**

30 m/s

Let the mass of the car be M. The forces on the car are

(a) weight Mg downward

(b) normal force N by the road upward

(c) friction fs by the road towards the centre

The car is going on a horizontal circle of radius R, so it is accelerating. The acceleration is towards the centre and its magnitude is v2R, where v is the speed. For vertical direction, acceleration = 0. Resolving the forces in vertical and horizontal directions and applying Newton's laws, we have

N = mg

and fs = Mv2R.

As we are looking for the maximum speed for no skidding, it is a case of limiting friction and hence

fs = μs N = μs Mg.

So, we have

μs Mg = Mv2R

or, v2 = μsgR.

Putting the values, v=√2×10m/s2×45m

= 30 m/s

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