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Find the maximum speed at which a truck can safely travel without toppling over, on a curve of radius $250 m$ . The height of the centre of gravity of the truck above the ground is $1.5 m$ and the distance between the wheels is $1.5 m$ , the truck being horizontal.

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$85 m / s$

$35 m / s$

$45 m / s$

$55 m / s$

answer is B.

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Detailed Solution

In critical case, normal reaction on inner wheel N, will become zero. Normal reaction on outer wheel $N_{e} = mg$ . Friction will provide the necessary centripetal force.

$∴ f = \frac{{mv}^{2}}{R}$

Taking moment about C.

$N_{0} (x) = f (h)$

$or (mg) x = (\frac{{mv}^{2}}{R}) h$

$∴ v = \sqrt{\frac{gRx}{h}}$

$= \sqrt{\frac{9.8 \times 250 \times 0.75}{15}}$

$= 35 m / s$

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