A car travels on a circular racetrack of radi | vedclass

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(A) For minimum wear and tear on the tyres, the car should travel at the optimum speed for the banked road, such that the normal force provides the ne

Vedclass · Accepted Answer

$	an^{-1}(1/5)$

Vedclass · Answer

(A) For minimum wear and tear on the tyres, the car should travel at the optimum speed for the banked road, such that the normal force provides the necessary centripetal force without relying on friction.The formula for the optimum speed $v$ on a banked road is given by $v = \sqrt{rg 	an 	heta}$.Squaring both sides, we get $v^2 = rg 	an 	heta$.Rearranging for $	an 	heta$, we have $	an 	heta = \frac{v^2}{rg}$.Given values are $v = 10 	ext{ ms}^{-1}$, $r = 50 	ext{ m}$, and $g = 10 	ext{ ms}^{-2}$.Substituting these values into the equation: $	an 	heta = \frac{10^2}{50 	imes 10} = \frac{100}{500} = \frac{1}{5}$.Therefore, $	heta = 	an^{-1}(1/5)$.

$A$ car travels on a circular racetrack of radius $50 \text{ m}$, which is banked at an angle $\theta$. If the car travels at a speed $10 \text{ ms}^{-1}$, then the wear and tear on its tyres is minimum. Taking the acceleration due to gravity to be $10 \text{ ms}^{-2}$, the value of $\theta$ is:

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