The correct option is
C 16 mThe equation of the surface is given by
y=x36.
Normal reaction on the block
(N) at a given point, will act
⊥ to the tangent to the curve at that point.
Static friction
(fs) will act in a tangential direction as shown in figure, to prevent the slipping of the block triggered by
mgsinθ component.
![](https://search-static.byjusweb.com/question-images/byjus/ckeditor_assets/pictures/914017/original_7.ii.png)
For maximum height of block on the surface without slipping, friction
fs will act at its limiting value.
fs=μsN ...(i) Applying equilibrium condition, along tangential and normal direction,
fs=mgsinθ ....(ii) N=mgcosθ ...(iii) Hence, from the above equations,
μsmgcosθ=mgsinθ ⇒tanθ=μs ...(iv) Slope of the surface represented by the equation
y=x36 is given by,
tanθ=dydx Or,
μs=16×3x2 ⇒0.5×63=x2 ∴x=√1=1 m Now, the maximum height for the block on the surface will correspond to a value of
x=1 m y=x36 ∴ymax=(1)36=16 m