What should be the maximum speed with which a car can be driven through a curve of radius $18 m$ without skidding (where, $g = 10 m s^{- 2}$ , coefficient of static friction between the rubber tyres and the roadway is $0.2$ )?

36.0 k m h^{- 1}

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18.0 k m h^{- 1}

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21.6 k m h^{- 1}

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14.4 k m h^{- 1}

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Solution

The correct option is C $21.6 k m h^{- 1}$
Given, $r = 18 m, g = 10 m s^{- 2}$
and $μ = 0.2$
Equation for dynamics of circular motion gives:
$\frac{m v_{m a x}^{2}}{r} = f = μ_{s} N = μ_{s} m g$
$v_{m a x} = \sqrt{μ_{s} r g} = \sqrt{0.2 \times 18 \times 10} = 6 m s^{- 1}$
Or, $6 \times \frac{18}{5} k m h^{- 1} = 21.6 k m h^{- 1}$

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What should be the maximum speed with which a car can be driven through a curve of radius 18 m without skidding (where, g=10 ms−2, coefficient of static friction between the rubber tyres and the roadway is 0.2)?

The correct option is C 21.6 kmh−1Given, r=18 m,g=10 ms−2 and μ=0.2 Equation for dynamics of circular motion gives: mv2maxr=f=μsN=μsmg vmax=√μsrg=√0.2×18×10=6 ms−1 Or, 6×185 kmh−1=21.6 kmh−1

What should be the maximum speed with which a car can be driven through a curve of radius $18 m$ without skidding (where, $g = 10 m s^{- 2}$ , coefficient of static friction between the rubber tyres and the roadway is $0.2$ )?