Question

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

• A. 172
• B. 124
• C. 99
• D. 86

Answer 1

Answer: (A)

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