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
B
32P
C
2P
D
22P

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 90So magnitude of resultant is $$2\sqrt { 2 } P$$  in direction of $${ 45 }^{ 0 }$$ from positive y axis in IV quadrant.Physics

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