On dry road, the maximum speed of a vehicle along a circular path is ' $\mathrm{V}$ '. When the road becomes…
On dry road, the maximum speed of a vehicle along a circular path is ' $\mathrm{V}$ '. When the road becomes wet, maximum speed becomes $\frac{V}{2}$. If coefficient of friction of dry road is ' $\mu$ ' then that of wet road is
$\frac{2 \mu}{3}$
$\frac{\mu}{4}$
$\frac{\mu}{3}$
$\frac{3 \mu}{4}$
Solution
The equation for maximum velocity is $\mathrm{V}=\sqrt{\mu \mathrm{rg}}$ ...(i)
When the road becomes wet the equation becomes
$\frac{\mathrm{V}}{2}=\sqrt{\mu^{\prime} \mathrm{rg}}$ ...(ii)
Dividing equation (i) with equation (ii),
$\begin{aligned}
& \frac{\frac{\mathrm{V}}{\mathrm{V}}}{2} \\
& =\frac{\sqrt{\mu \mathrm{rg}}}{\sqrt{\mu^{\prime} \mathrm{rg}}} \\
\therefore \quad 2 & =\frac{\sqrt{\mu}}{\sqrt{\mu^{\prime}}} \\
\therefore \quad \mu^{\prime} & =\frac{\mu}{4}
\end{aligned}$