Question

A solid cube of mass $5kg$ is placed on a rough horizontal surface, in $xy-$plane as shown. The friction coefficient between the surface and the cube is $0.4$. An external force
$\overrightarrow{F}=6\hat{i}+8\hat{j}+20\hat{k}N$ is applied on the cube.(use $g=10m/s^2$ )

• A. The block starts slipping over the surface
• B. The friction force on the cube by the surface is $10N$
• C. The friction force acts in $xy-$plane at angle ${127}^0$ with the positive $x-$ axis in clockwise direction
• D. The contact force exeerted by the surface on the cube is $10\sqrt{1}0N$

Answer 1

The correct option is A The block starts slipping over the surface

Given, external force $\overrightarrow{F}=6\hat{i}+8\hat{j}+20\hat{k}N$
$F=\sqrt{6^2+8^2+{20}^2}=\sqrt{500}=22.36N$
and $F_s=\mu N$
$F_s=0.4\times 5\times 10=20N$
Since $F_s<F$, the cube will slide.