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Solve the following :


A car goes on a horizontal circular road of radius $\mathrm{R}$, the speed increasing at a constant rate $\mathrm{dv} / \mathrm{dt}=$ a. The friction dt coefficient between the road and the tyre is $\mu$. Find the speed at which the car will skid.


From free body diagram


$\mu \mathrm{N}=\sqrt{(m a)^{2}+\left(\frac{m v^{2}}{R}\right)^{2}}$

$(\mu \mathrm{mg})=\sqrt{(m a)^{2}+\left(\frac{m v^{2}}{R}\right)^{2}}$

Squaring and solving,

$V=\left[\left(\mu^{2} g^{2}-a^{2}\right) R^{2}\right]^{1 / 4}$

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