Q109 / 150 · MHT CET 2023 (14 May Shift 1) · Physics
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
- A$\frac{2 \mu}{3}$
- Correct answerB$\frac{\mu}{4}$
- C$\frac{\mu}{3}$
- D$\frac{3 \mu}{4}$
Solution
The equation for maximum velocity is $\mathrm{V}=\sqrt{\mu \mathrm{rg}}$
When the road becomes wet the equation becomes
$$
\frac{\mathrm{V}}{2}=\sqrt{\mu^{\prime} \mathrm{rg}}
$$
Dividing equation (i) with equation (ii),
$$
\begin{aligned}
& \frac{\mathrm{V}}{\mathrm{V}} \\
& =\frac{\sqrt{\mu \mathrm{rg}}}{\sqrt{\mu^{\prime} \mathrm{rg}}} \\
\therefore \quad 2 & =\frac{\sqrt{\mu}}{\sqrt{\mu^{\prime}}} \\
\therefore \quad \mu^{\prime} & =\frac{\mu}{4}
\end{aligned}
$$
Hence, the correct answer is option: 'B'.