Q 11-04-082JEE MainJEE Main 2024 (6 Apr, Shift 2)Medium
A car of $800\ \text{kg}$ is taking a turn on a banked road of radius $300\ \text{m}$ and angle of banking $30^\circ$. If the coefficient of static friction is $0.2$, then the maximum speed with which the car can negotiate the turn safely is ($g = 10\ \text{m/s}^2$, $\sqrt3 = 1.73$)
Answer: (B) $51.4\ \text{m/s}$
$$v_{max}^2 = rg\,\frac{\tan\theta + \mu}{1 - \mu\tan\theta} = 300\times10\times\frac{0.577 + 0.2}{1 - 0.2\times0.577} = 3000\times\frac{0.777}{0.885} \approx 2636$$
$$v_{max} \approx 51.4\ \text{m/s}$$
Solution by Sreeraj P, M.Sc Physics