A block takes t time to slide down a plane inclined at 45° to the horizontal. If the surface is made smooth (frictionless), the block takes time t/2 to slide down the plane. The coefficient of friction between the block and the inclined plane is ((α)/(100)). The value of α is ______. Numerical answer type. Work it out, then open the answer.

Answer: 75. At 45°, same distance: (tr)/(ts) = (1)/(√(1-μ)). t/t/2 = 2 ⇒ 1 - μ = 1/4 ⇒ μ = 0.75 = 75/100 α = 75

A block takes t time to slide down a plane inclined at 45° to the… | JEE Main 2026 (6 Apr, Shift 2)

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Friction on an Incline

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 $\frac{t}{2}$ to slide down the plane. The coefficient of friction between the block and the inclined plane is $\left(\frac{\alpha}{100}\right)$ . The value of $\alpha$ is ______.

Numerical answer type. Work it out, then open the answer.

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Answer: 75

At $45^\circ$ , same distance: $\dfrac{t_r}{t_s} = \dfrac{1}{\sqrt{1-\mu}}$ .
$\dfrac{t}{t/2} = 2 \Rightarrow 1 - \mu = \dfrac{1}{4} \Rightarrow \mu = 0.75 = \dfrac{75}{100}$
$\alpha = 75$

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