Q 11-04-162JEE MainJEE Main 2021 (24 Feb, Shift 1)Medium
An inclined plane is bent in such a way that the vertical cross-section is given by $y = \dfrac{x^2}{4}$ where $y$ is in vertical and $x$ in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction $\mu = 0.5$, the maximum height in cm at which a stationary block will not slip downward is ______ cm.
Numerical value type. Enter your answer.
Answer: 25
A block stays at rest as long as the local slope satisfies $\tan\theta \le \mu$.
$$\tan\theta = \frac{dy}{dx} = \frac{x}{2} \le 0.5 \;\Rightarrow\; x \le 1\ \text{m}$$
$$y_{max} = \frac{1^2}{4} = 0.25\ \text{m} = 25\ \text{cm}$$
Solution by Sreeraj P, M.Sc Physics