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  • An inclined plane is bent in such a way that the vertical cross-section is given by  where y is in vertical and x in horizo

An inclined plane is bent in such a way that the vertical cross-section is given by y = \frac{x^2}{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 \mu = 0.5, the maximum height in cm at which a stationary block will not slip downard is _________cm.
Option: 1 25
Option: 2 -
Option: 3 -
Option: 4 -

Answers (1)

best_answer

\\ \text{At maximum height block will experience maximum friction force.}\\ \text{Therefore if at this height slope of the tangent is} \tan \theta, \\ then \ \theta= \text{Angle of repose.}\\\\ \therefore \tan \theta=\frac{d y}{d x}=\frac{2 x}{4}=\frac{x}{2}\\\\ \mu=tan \theta=0.5 \Rightarrow x=1 \\ \text{and therefore}\ y=\frac{x^{2}}{4}=0.25 \mathrm{~m}=25 cm

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