Mathematics in Physics

JEE Main level, single correct, medium

21 of 121

Question 21 of 121

The resultant of these forces OP⃗,OQ⃗,OR⃗,OS⃗\vec{OP},\vec{OQ},\vec{OR},\vec{OS} and OT⃗\vec{OT} is approximately ______N.N.
[Take 3=1.7,2=1.4\sqrt{3}=1.7,\sqrt{2}=1.4 Given i^\hat{i} and j^\hat{j} unit vectors along x,yx,y axis]

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Answer: (B) 9.25i^+5j^9.25\hat{i}+5\hat{j}

Resultant (R⃗)=i^(10cos⁡30∘+20cos⁡60∘−15cos⁡30∘−15cos⁡45∘+20cos⁡45∘)(\vec{R})=\hat{i}\left(10\cos 30^{\circ}+20\cos 60^{\circ}-15\cos 30^{\circ}-15\cos 45^{\circ}+20\cos 45^{\circ}\right)
+j^(10sin⁡30∘+20sin⁡60∘+15sin⁡30∘−15sin⁡45∘−20cos⁡45∘)+\hat{j}\left(10\sin 30^{\circ}+20\sin 60^{\circ}+15\sin 30^{\circ}-15\sin 45^{\circ}-20\cos 45^{\circ}\right)
=9.25i^+5j^=9.25\hat{i}+5\hat{j}

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