A circular road of radius 1000 , m has a bank | vedclass

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(A) The formula for the maximum safe speed $v$ on a banked road with friction is given by:$v = \sqrt{gr \left( \frac{\mu + 	an 	heta}{1 - \mu 	an \

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$172$

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(A) The formula for the maximum safe speed $v$ on a banked road with friction is given by:$v = \sqrt{gr \left( \frac{\mu + 	an 	heta}{1 - \mu 	an 	heta} ight)}$Given values are:Radius $r = 1000 \, m$Banking angle $	heta = 45^\circ$Coefficient of friction $\mu = 0.5$Acceleration due to gravity $g = 9.8 \, m/s^2$Substituting these values into the formula:$v^2 = 9.8 	imes 1000 	imes \left( \frac{0.5 + 	an 45^\circ}{1 - 0.5 	imes 	an 45^\circ} ight)$Since $	an 45^\circ = 1$:$v^2 = 9800 	imes \left( \frac{0.5 + 1}{1 - 0.5 	imes 1} ight)$$v^2 = 9800 	imes \left( \frac{1.5}{0.5} ight)$$v^2 = 9800 	imes 3 = 29400$$v = \sqrt{29400} \approx 171.46 \, m/s \approx 172 \, m/s$.

$A$ circular road of radius $1000 \, m$ has a banking angle of $45^\circ$. The maximum safe speed of a car having mass $2000 \, kg$ will be,if the coefficient of friction between the tyre and road is $0.5$,equal to ....... $m/s$.

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