Question

In the figure shown, if the block does not slide down the plane when a force of $\text{10 N}$ is applied perpendicular to the plane, find the coefficient of static friction between the plane and the block.(Consider limiting case of friction) Take $g={\text{10 m/s}}^2.$

• A. $\frac{1}{\sqrt{2}}$
• B. $\frac{1}{2}$
• C. $\frac{1}{3}$
• D. $\frac{1}{\sqrt{3}}$

Answer 1

The correct option is D $\frac{1}{\sqrt{3}}$

FBD of the block


$\text{10 N}$ force is perpendicular to the plane and its own weight also has a component of $mg\cos \theta$ in the same direction
Net normal force perpendicular to the plane:
$N=10+5=15\text{N}$
Block is in equilbrium. So, along the plane,
$f=10\sin {60}^{\circ }=5\sqrt{3}$
For limiting case
$f=f_L=\mu N=\mu \times 15$
$\Rightarrow \mu \times 15=5\sqrt{3},\Rightarrow \mu =\frac{1}{\sqrt{3}}$