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://df0b18phdhzpx.cloudfront.net/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