Question

A block kept on a rough inclined plane as shown in the figure, remains at rest upto a maximum force $2N$ down the inclined plane. The maximum external force up the inclined plane that does not move the block is $10N$. The coefficient of static friction between the block and the plane is
[Take $g=10m/s^2]$

• A. $\frac{\sqrt{3}}{2}$
• B. $\frac{2}{3}$
• C. $\frac{1}{2}$
• D. $\frac{\sqrt{3}}{4}$

Answer 1

The correct option is A $\frac{\sqrt{3}}{2}$

Case 1: When maximum force of $2N$ down the plane holds the block at rest.

$f=\mu N=\mu mg\cos {30}^{\circ }$
From the FBD,
$\begin{array}{}2+mg\sin {30}^{\circ }=\mu mg\cos {30}^{\circ }& \text{(1)}\end{array}$

Case 2: When maximum force of $10N$ up the plane holds the block at rest.

$10=mg\sin {30}^{\circ }+\mu mg\cos {30}^{\circ }$
Using equation $\left(1\right)$,
so, $10=\frac{mg}{2}+2+\frac{mg}{2}$
$\Rightarrow mg=8$
from $\left(1\right)$
$2+8\times \frac{1}{2}=\mu \times 8\times \frac{\sqrt{3}}{2}$
$\mu =\frac{12}{8\sqrt{3}}=\frac{\sqrt{3}}{2}$
The correct option is (B).