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QJEEM21Ph518a: JEE Main 2021 Physics - Class 11 JEEM21Ph518a Solution: An inclined plane is bent in such a way that the vertical…

An inclined plane is bent in such a way that the vertical cross-section is given by y=x24y = {{{x^2}} \over 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 μ\mu = 0.5, the maximum height in cm at which a stationary block will not slip downward is _________ cm.

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JEE Main 2021 (Online) 24th February Morning Shift Physics - Laws of Motion Question 90 English Explanation
At maximum height, the slope of tangent drawn,

tan⁡θ=dydx=2x4=x2\tan \theta = {{dy} \over {dx}} = {{2x} \over 4} = {x \over 2} [ ∵\because y=x24y = {{{x^2}} \over 4} ]

⇒0.5=x2\Rightarrow 0.5 = {x \over 2} ( ∵\because μ\mu = tan θ\theta )

⇒\Rightarrow x = 1 m

∴\therefore y=x24=14y = {{{x^2}} \over 4} = {1 \over 4} = 0.25 m = 25 cm

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