QJEEM14Ph5181: JEE Main 2014 Physics - Class 11 JEEM14Ph5181 Solution: A block of mass m is placed on a surface with a vertical cross…

Question

Verified Solution • 2025–26 Session moderate

A block of mass

m

is placed on a surface with a vertical cross section given by

y = \frac{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:

Accepted Answer

At limiting equilibrium,

μ = \tan θ

Equation of the surface,

y = \frac{x^{3}}{6}

Slope,

\tan θ = μ = \frac{d y}{d x} = \frac{x^{2}}{2}

Given that, Coefficient of friction

μ = 0.5

∴

0.5 = \frac{x^{2}}{2}

\Rightarrow x = \pm 1

Now,

y = \frac{x^{3}}{6} = \frac{1}{6} m

Step-by-Step Verified Solution