Question

Three particles of masses $1\text{kg},2\text{kg}$ and $3\text{kg}$ are subjected to forces $(3\hat{i}-2\hat{j}+2\hat{k})\text{N}$, $(-\hat{i}+2\hat{j}-\hat{k})\text{N}$ and $(\hat{i}+\hat{j}+\hat{k})\text{N}$ respectively. The magnitude of the acceleration of the CM of the system is -

• A. $\frac{\sqrt{11}}{6}{\text{m/s}}^2$
• B. $\frac{\sqrt{14}}{6}{\text{m/s}}^2$
• C. $\frac{11}{6}{\text{m/s}}^2$
• D. $\frac{22}{6}{\text{m/s}}^2$

Answer 1

The correct option is B $\frac{\sqrt{14}}{6}{\text{m/s}}^2$

$F_{net}=F_1+F_2+F_3$
$=(3\hat{i}-2\hat{j}+2\hat{k})+(-\hat{i}+2\hat{j}-\hat{k})+(\hat{i}+\hat{j}+\hat{k})$
$F_{net}=(3\hat{i}+\hat{j}+2\hat{k})\text{N}$

Total mass of the system, $M=1+2+3=6\text{kg}$

$\therefore$ acceleration of the COM of the system
${\overrightarrow{a}}_{COM}=\frac{F_{net}}{M}=\frac{3\hat{i}+\hat{j}+2\hat{k}}{6}$
i.e $a_{COM}=\frac{\sqrt{3^2+1^2+2^2}}{6}=\frac{\sqrt{14}}{6}{\text{m/s}}^2$