JEE Main 2026 Apr 6 Shift 2, Physics Q21: Friction

JEE Main2026Apr 6, Shift 2Physics

A block takes $t$ time to slide down a plane inclined at $4 5^{\circ}$ 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 $(\frac{α}{100})$ . The value of $α$ is ____.

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Solution

On rough incline at $4 5^{\circ}$ : $a_{1} = g sin 4 5^{\circ} - μg cos 4 5^{\circ} = \frac{g}{2} (1 - μ)$ .

On smooth incline: $a_{2} = g sin 4 5^{\circ} = \frac{g}{2}$ .

Same length, $L = \frac{1}{2} a_{1} t^{2} = \frac{1}{2} a_{2} (t /2)^{2}$ gives $a_{1} t^{2} = a_{2} \frac{t ^{2}}{4}$ $\Rightarrow$ $a_{1} = \frac{a _{2}}{4}$ .

$1 - μ = \frac{1}{4}$ $\Rightarrow$ $μ = \frac{3}{4} = \frac{75}{100}$ , so $α = 75$ .

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JEE Main 2026 Apr 6 Shift 2, Physics Q21: Friction

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