Question

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. 1/2 m
• B. 1/6 m
• C. 2/3 m
• D. 1/3 m

Answer 1

Answer: (B)

1/6 m

Block is under limiting friction, so
$\mu =tan\theta$ ..........(i)
Equation of the surface,
$y=\frac{x^3}{6}$
Slope, $\frac{dy}{dx}=\frac{x^2}{2}$ ...........(ii)
From eqns (i) and (ii), we get
$\mu =\frac{x^2}{2}\Rightarrow 0.5=\frac{x^2}{2}\Rightarrow x^2=1\Rightarrow x=1.$
So, $y=\frac{1}{6}$