Question

Five forces $\overrightarrow{F_1},\overrightarrow{F_2},\overrightarrow{F_3},\overrightarrow{F_4}$ and $\overrightarrow{F_5}$ are acting on a particle of mass $2.0\text{kg}$ so that it is moving with $4{\text{m/s}}^2$ in east direction. If $\overrightarrow{F_1}$ force is removed then the acceleration becomes $7{\text{m/s}}^2$ in north. Find the magnitude of acceleration of the block if only $\overrightarrow{F_1}$ is acting.

• A. $16{\text{m/s}}^2$
• B. $\sqrt{65}{\text{m/s}}^2$
• C. $\sqrt{260}{\text{m/s}}^2$
• D. $\sqrt{33}{\text{m/s}}^2$

Answer 1

The correct option is B $\sqrt{65}{\text{m/s}}^2$

$\overrightarrow{F_1}+\overrightarrow{F_2}+\overrightarrow{F_3}+\overrightarrow{F_4}+\overrightarrow{F_5}=2\left(4\hat{i}\right)\left(i\right)$
and $\overrightarrow{F_2}+\overrightarrow{F_3}+\overrightarrow{F_4}+\overrightarrow{F_5}=2\left(7\hat{j}\right)\left(ii\right)$
From $\left(i\right)$ and $\left(ii\right)$, $\overrightarrow{F_1}=8\hat{i}-14\hat{j}$
$\overrightarrow{a_1}=\frac{\overrightarrow{F_1}}{m}=4\hat{i}-7\hat{j}$
$\Rightarrow a_1=\sqrt{16+49}=\sqrt{65}{\text{m/s}}^2$