A car of $800 \mathrm{~kg}$ is taking turn on a banked road of radius $300 \mathrm{~m}$ and angle of banking $30^{\circ}$. If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely: $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \sqrt{3}=1…

Question

A car of $800 \mathrm{~kg}$ is taking turn on a banked road of radius $300 \mathrm{~m}$ and angle of banking $30^{\circ}$. If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely: $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \sqrt{3}=1.73\right)$

Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{m}=800 \mathrm{~kg} \ & \mathrm{r}=300 \mathrm{~m} \ & 	heta=30^{\circ} \ & \mu_{\mathrm{s}}=0.2 \ & \mathrm{~V}_{\max }=\sqrt{\operatorname{Rg}\left[\frac{	an 	heta+\mu}{1-\mu 	an 	heta}ight]} \ & =\sqrt{300 	imes \mathrm{g} 	imes\left[\frac{	an 30^{\circ}+0.2}{1-0.2 	imes 	an 30^{\circ}}ight]} \ & =\sqrt{300 	imes 10 	imes\left[\frac{0.57+0.2}{1-0.2 	imes 0.57}ight]} \ & \mathrm{V}_{\max }=51.4 \mathrm{~m} / \mathrm{s}\end{aligned}$

A car of $800 \mathrm{~kg}$ is taking turn on a banked road of radius $300 \mathrm{~m}$ and angle of banking…

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