Question

A circular road of radius 1000 m has banking angle ${45}^0$. The maximum safe speed (in ms^{-1}$) of a car having a mass 2000 kg will be (if the coefficient of friction between tyre and road is 0.5)

• A. 172
• B. 124
• C. 99
• D. 86

Answer 1

The correct option is A 172

From FBD $N=\frac{mg}{\sqrt{2}}+\frac{m{v}^2}{R\sqrt{2}}$ and $\frac{mg}{\sqrt{2}}+f=\frac{m{v}^2}{R\sqrt{2}}f=\mu N\Rightarrow \frac{\mu mg}{\sqrt{2}}+\frac{\mu m{v}^2}{R\sqrt{2}}+\frac{mg}{\sqrt{2}}=\frac{m{v}^2}{R\sqrt{2}}\Rightarrow \mu mgR+\mu m{v}^2+mgR=m{v}^2\Rightarrow mgR(\mu +1)=m{v}^2(1-\mu )\Rightarrow v^2=gR\frac{(\mu +1)}{1-\mu }=10\times 1000\times \frac{\left(1.5\right)}{0.5}=(\sqrt{3}{)}^2\times (100{)}^2\therefore v=172$