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?

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

$\sqrt{2} N, 135^{\circ}$

$\frac{2}{\sqrt{3}} N, 30^{\circ}$

$2 N, 45^{\circ}$

answer is A.

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Detailed Solution

$Let addiction force required is = \vec{F} \begin{array}{l} \vec{F} + 5 \hat{i} - 6 \hat{i} + 7 \hat{j} - 8 \hat{j} = 0 \\ \vec{F} = \hat{i} + \hat{j}, | \vec{F} | = \sqrt{2} \end{array} Angle with x - axis : \tan θ = \frac{y component}{x component} = \frac{1}{1} θ = 45 °$

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