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. $2 N , 45^{\circ}$

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: $\tan \theta=\frac{ y \text { component }}{ x \text { component }}=\frac{1}{1}$
$\theta=45^{\circ}$