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# A Wheeled vehicle travels around a circular track of radius $50\;m$ The wheels are $2m$ apart(side ways) and the center of gravity is $0.8 m$ above the ground. The coefficient of friction is $0.4$ . Determine whether it overturns or slides sideways and determine the velocity at which it occurs ?

$\begin{array}{1 1} \text{It skids first when velocity =14 m/s} \\ \text{It overturns when velocity =14 m/s} \\ \text{ It skids when the velocity =24.76 m/s}\\ \text{It overturns first when the velocity =24.76 m/s}\end{array}$

Overturning $v= (gdR/h)^{1/2} =(9.81 \times 1 \times 50/0.8 )^{1/2}$
$\qquad= 24.76 \;m/s$
Sliding sideways $v= (\mu gR)^{1/2}$
$\qquad= (0.4 \times 9.81 \times 50)^{1/2}$
$\qquad= 14 m/s$
It follows that it will slide sideways when the velocity reaches $14\; m/s$