Q 11-04-054JEE MainJEE Main 2026 (6 Apr, Shift 2)Medium
A block takes $t$ time to slide down a plane inclined at $45^\circ$ to the horizontal. If the surface is made smooth (frictionless), the block takes time $\dfrac{t}{2}$ to slide down the plane. The coefficient of friction between the block and the inclined plane is $\left(\dfrac{\alpha}{100}\right)$. The value of $\alpha$ is ______.
Numerical value type. Enter your answer.
Answer: 75
For the same distance from rest, $t \propto \dfrac{1}{\sqrt{a}}$. Halving the time means the smooth acceleration is $4$ times the rough one:
$$g\sin 45^\circ = 4g(\sin 45^\circ - \mu\cos 45^\circ) \;\Rightarrow\; 1 = 4(1 - \mu) \;\Rightarrow\; \mu = 0.75$$
$\alpha = 75$.
Solution by Sreeraj P, M.Sc Physics