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Question

Four forces of magnitude P, 2P, 3P and 4P act along the four sides of a square ABCD in cyclic order. Use the vector method to find the resultant force.


A
22P
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B
32P
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C
2P
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D
22P
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Solution

The correct option is A $$\displaystyle 2\sqrt{2}P$$
The resultant of 4 vectors in X, Y direction are:
resultant in X direction is 
$$3\vec P - \vec P = 2\vec P $$      (in -ve x direction)
In y direction is
$$4\vec P - 2\vec P = 2\vec P$$     (in +ve y direction)

So, the net resultant force vector is 
$$\overset { \rightarrow  }{ R } =2\overset { \rightarrow  }{ P } +2\overset { \rightarrow  }{ P } $$
angle between both vectors is 90
So magnitude of resultant is $$2\sqrt { 2 } P$$  in direction of $${ 45 }^{ 0 }$$ from positive y axis in IV quadrant.

554652_206922_ans.png

Physics

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