A car of 800 kg is taking turn on a banked road of radius 300 m and angle of banking 30°. If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely is

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Solution

Q.
A car of 800 kg is taking turn on a banked road of radius 300 m and angle of banking 30°. If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely is $(g = 10 m / s^{2}, \sqrt{3} = 1.73)$ [2024]

1 51.4 m/s

2 102.8 m/s

3 70.4 m/s

4 264 m/s

Ans.
(1)

$V_{m a x} = \sqrt{R g [\frac{\tan θ + μ}{1 - μ \tan θ}]} = \sqrt{300 \times 10 [\frac{\tan 30^{o} + 0.2}{1 - 0.2 \tan 30^{o}}]}$

$V_{m a x} = \sqrt{3000 [\frac{\frac{1}{\sqrt{3}} + 0.2}{1 - 0.2 (\frac{1}{\sqrt{3}})}]} = \sqrt{\frac{3000 \times 0.77}{0.88}} = \sqrt{2625}$

$\Rightarrow V_{m a x} = 51.3 m / s e c$

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