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

The Truck will topple about the outer wheels. let the height of the center of gravity be h, the distance between the tyres be d, and the radius of curvature be R, for toppling the maximum speed is given by,(equating the torque by gravity and torque by centrifugal force about the outer wheel) $\dfrac{m{ { v }_{ max } }^{ 2 } }{ R } h=mg\dfrac { d }{ 2 }$

$\Rightarrow { v }_{ max }=\sqrt { \dfrac { Rgd }{ 2h } } =35.35m/s$