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

$2 N, 45^{o}$

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

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

answer is A.

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Detailed Solution

$F = 5 \hat{i} - 6 \hat{i} + 7 \hat{j} - 8 \hat{j} F = - \hat{i} - \hat{j} = 0 F = \hat{i} + \hat{j} |F| = \sqrt{1^{2} + 1^{2}} = \sqrt{2}; \tan θ = \frac{y}{x} = \frac{1}{1}; θ = \tan^{- 1} (1) = 45^{o}$

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