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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.


A

20 m/s

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B

30 m/s

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C

10 m/s

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D

40 m/s

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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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