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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Answer & Solution

Correct Answer

(A) \(\sqrt{2} N , 45^{\circ}\)

Step-by-step Solution

Detailed explanation

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: \(\tan \theta=\frac{ y \text { component }}{ x \text { component }}=\frac{1}{1}\)

\(\theta=45^{\circ}\)

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