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. Take $g=10m/s^2$

• 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 can be shown as


Perpendicular to the plane $\Sigma F_y=0$
$\Rightarrow N=10+10\cos {60}^{\circ }=15\text{N}$
Along the plane, since block is at rest
$\Rightarrow a=0$
So, we have the force equation as
$10\sin {60}^{\circ }=f=\mu N\Rightarrow \mu =\frac{10\sin {60}^{\circ }}{N}$
$\Rightarrow \mu =\frac{10\sin {60}^{\circ }}{15}=\frac{10\sqrt{3}}{15\times 2}=\frac{1}{\sqrt{3}}$