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JEE Main 202124 FebruaryMorning Shift
Exam
JEE Main
Year
2021
Date
24 February
Shift
Morning Shift
Subject
Physics
Chapter
Laws of Motion

JEE Main 2021 · 24 February · Morning Shift · Physics · Laws of Motion

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 = \dfrac{{x}^{2}}{4} where yy is in vertical and xx in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction μ=0.5,\mu = 0 . 5, the maximum height in cmcm at which a stationary block will not slip downward is________cm.cm .An inclined plane is bent in such a way that the vertical cross-section is given by y = x ^ 2 4 where y is in vertical

Correct answer

0

Step-by-step solution

An inclined plane is bent in such a way that the vertical cross-section is given by y = x ^ 2 4 where y is in vertical

At maximum ht. block will experience maximum friction force. Therefore if at this height slope of the tangent is tanθ,tan\theta, then θ=\theta =Angle of repose

∴tanθ=dydx=2x4=x2=0.5∴ tan\theta = \dfrac{dy}{dx} = \dfrac{2x}{4} = \dfrac{x}{2} = 0 . 5

⇒x=1⇒ x = 1 and therefore y=x24=0.25my = \dfrac{{x}^{2}}{4} = 0 . 25m

=25cm= 25cm

∴∴ Answer is 25cm25cm

(Assuming that xx & yy in the equation are given in meter)

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