Question

A block of mass $m$ is placed on a surface with a vertical height 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. $\frac{1}{3}m$
• B. $\frac{1}{2}m$
• C. $\frac{1}{6}m$
• D. $\frac{2}{3}m$

Answer 1

The correct option is C $\frac{1}{6}m$

By balancing the forces, we get
$mgsin\theta =\mu mgcos\theta$
$tan\theta =\mu$
$\frac{dy}{dx}=tan\theta =\mu =\frac{1}{2}$
$\frac{x^2}{2}=\frac{1}{2},x=\pm 1$
putting value of $x$ in equation of $y$,
$y=\frac{1}{6}m$.