Question

A block of mass $5\text{kg}$ is kept on a horizontal floor having coefficient of friction 0.09. Two mutually perpendicular horizontal forces of 3 N and 4 N act on this block. The acceleration of the block is: ($g=10{\text{m/s}}^2$)

• A. Zero
• B. $0.1{\text{m/s}}^2$
• C. $0.2{\text{m/s}}^2$
• D. $0.3{\text{m/s}}^2$

Answer 1

The correct option is B $0.1{\text{m/s}}^2$

Net external force $F=\sqrt{(4{)}^2+(3{)}^2}=5N$
Maximum friction $f_{max}=\mu mg=\left(0.09\right)\left(5\right)\left(10\right)=4.5N$
Since $F>f_{max}$, block will move with an acceleration,
$a=\frac{F-f_{max}}{m}=\frac{5-4.5}{5}=0.1{\text{m/s}}^2$