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 : $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \sqrt{3}=1.73\right)$
JEE MAIN 2024, Difficult
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$\mathrm{m}=800 \mathrm{~kg}$
$\mathrm{r}=300 \mathrm{~m}$
$\theta=30^{\circ}$
$\mu_2=0.2$
$\mathrm{~V}_{\max }=\sqrt{\operatorname{Rg}\left[\frac{\tan \theta+\mu}{1-\mu \tan \theta}\right]}$
$=\sqrt{300 \times \mathrm{g} \times\left[\frac{\tan 30^{\circ}+0.2}{1-0.2 \times \tan 30^{\circ}}\right]}$
$=\sqrt{300 \times 10 \times\left[\frac{0.57+0.2}{1-0.2 \times 0.57}\right]}$
$\mathrm{V}_{\max }=51.4 \mathrm{~m} / \mathrm{s}$
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