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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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