Question

A body of mass $20kg$ is kept on a rough horizontal surface. If ${\mu }_s=0.5$ and an external force of $F=50N$ is applied on the body, find the contact force on the body. (Take $g=10m/s^2$)

• A. $\text{Zero}$
• B. $50\sqrt{17}N$
• C. $100\sqrt{5}N$
• D. $200N$

Answer 1

The correct option is B $50\sqrt{17}N$

The given condition can be considered as shown

$\Sigma F_y=0$
$\Rightarrow N=mg=20g=200N$
and, $f={\mu }_{s}N={\mu }_{s}mg=0.5\times 200=100N$
$\therefore$ Contact force $R=\sqrt{N^2+f^2}=\sqrt{{200}^2+{50}^2}=50\sqrt{17}N$