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 $2.0kg$ so that it is moving with $4m/s^2$ in east direction. If ${\overrightarrow{F}}_1$ force is removed, then the acceleration of the particle becomes $7m/s^2$ in north. If the acceleration of the particle is $\sqrt{n}m/s^2$ if only ${\overrightarrow{F}}_1$ is acting, then find $n$.

Answer 1

Let mass of the particle be 𝑚. Then
$\frac{{\overrightarrow{F}}_1+{\overrightarrow{F}}_2+{\overrightarrow{F}}_3+{\overrightarrow{F}}_4+{\overrightarrow{F}}_5}{m}=4\hat{i}$ ;
$\frac{F_2+{\overrightarrow{F}}_3+{\overrightarrow{F}}_4+{\overrightarrow{F}}_5}{m}=7\hat{j}$ ;
$\frac{{\overrightarrow{F}}_1}{m}=4\hat{i}-7\hat{j}$

$\frac{{\overrightarrow{F}}_1}{m}=$Acceleration due to ${\overrightarrow{F}}_1$
$|\frac{{\overrightarrow{F}}_1}{m}|=\sqrt{4^2+7^2}=\sqrt{65}m/s^2$
Final Answer: $65$