The radius of a curved road on a national hig | vedclass

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(A) For a vehicle to negotiate a curved road of radius $R$ safely without relying on friction,the road is banked at an angle $	heta$. From the dynami

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$\frac{v^2 b}{Rg}$

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(A) For a vehicle to negotiate a curved road of radius $R$ safely without relying on friction,the road is banked at an angle $	heta$. From the dynamics of circular motion,the condition for safe banking is given by $	an 	heta = \frac{v^2}{Rg}$. From the geometry of the banked road,where $h$ is the height of the outer edge and $b$ is the width of the road,we have $	an 	heta = \frac{h}{b}$ (assuming $	heta$ is small). Equating the two expressions for $	an 	heta$: $\frac{h}{b} = \frac{v^2}{Rg}$ Therefore,the height $h$ is given by $h = \frac{v^2 b}{Rg}$.

The radius of a curved road on a national highway is $R$. The width of the road is $b$. The outer edge of the road is raised by $h$ with respect to the inner edge so that a car with velocity $v$ can pass safely over it. The value of $h$ is

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