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A vehicle whose wheel track is $1.7 m$ wide and whose centre of gravity is $1 m$ above the road and centre between the wheels, takes a curve whose radius is $50 m$ , on a level road. Find the speed at which the inner wheel would leave the road.

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$29.41 m / s$

$20.4 m / s$

$23.4 m / s$

$18.4 m / s$

answer is A.

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Detailed Solution

To prevent overturning of the vehicle, we have

$v \leq \sqrt{\frac{r g a}{h}}$

Here $r = 50 m, a = \frac{1.7}{2} = 0.85 m$ and $h = 1 m$ .

$∴ v = \sqrt{\frac{50 \times 9.8 \times 0.85}{1}} = 20.40 m / s$

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