A block of mass m is placed on a surface with a vertical cross- section given by y = x^(3)/6. If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is

A block of mass m is placed on a surface with a vertical cross- sectio

1.	A block of mass m is placed on a surface with a vertical cross- section given by y = x^(3)/6. If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is
Answer» `(1)/(6)` m `(2)/(3)`m `(1)/(3)`m `(1)/(2)`m Solution :Angle of REPOSE, `theta = tan^(-1) mu "" or, tan theta = 0.5`. The surface y = `(X^(3))/(6)` is curved. At any point on it, tan`theta = (dy)/(dx) = (3X^(2))/(6) = (x^(2))/(2)or, (x^(2))/(2) = 0.5 ` `therefore` x = 1 So, maximum height, `y_(m) = (1^(3))/(6) = (1)/(6) m`