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 and x in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction μ = 0 . 5 , the maximum height in cm at which a stationary block will not slip downward is________ cm .

Step-by-step solution

At maximum ht. block will experience maximum friction force. Therefore if at this height slope of the tangent is tan θ , then θ = Angle of repose ∴     tan θ = d y d x = 2 x 4 = x 2 = 0 . 5 ⇒ x = 1 and therefore y = x 2 4 = 0 . 25   m = 25   cm ∴ Answer is 25   cm (Assuming that x & y in the equation are given in meter)