Question

For a free body diagram shown in the figure, the four forces are applied in the ' $x$ ' and ' $y$ ' directions. What additional force must be applied and at what angle with positive $x$-axis so that the net acceleration of body is zero?

• A. $\sqrt{2}N,45^{\circ }$
• B. $\sqrt{2}N,135^{\circ }$
• C. $\frac{2}{\sqrt{3}}N,30^{\circ }$
• D. $2N,45^{\circ }$

Answer 1

Answer: (A)

Let addition force required is $=\overrightarrow{F}$
$\overrightarrow{F}+5\hat{i}-6\hat{i}+7\hat{j}-8\hat{j}=0$
$\overrightarrow{F}=\hat{i}+\hat{j},|\overrightarrow{F}|=\sqrt{2}$
Angle with $x$-axis: $\tan \theta =\frac{y\text{ component }}{x\text{ component }}=\frac{1}{1}$
$\theta =45^{\circ }$