Question

Find the acceleration (in $m/s^2$) of the body of mass $20kg$ shown in the figure. Take $g=10m/s^2$.

• A. $0.33$
• B. $6.4$
• C. $10$
• D. $\text{Zero}$

Answer 1

The correct option is D $\text{Zero}$

The FBD of the block is

$\Sigma F_y=0$
$N+F\sin {30}^{\circ }=mg\Rightarrow N=20g-100\sin {30}^{\circ }=200-50=150N$
$\therefore$ $f_{max}={\mu }_{s}N=0.6\left(150\right)=90N$

Total Applied driving force on the block is
$F^{{}^{\prime }}=F\cos {30}^{\circ }=\frac{100\sqrt{3}}{2}=50\sqrt{3}N$
$=86.6N$
Since, $F^{{}^{\prime }}<f_{max}$, the block will be at rest.
Thus, the acceleration of the body will be zero.