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. $2\sqrt{2}P$
• B. $3\sqrt{2}P$
• C. $\sqrt{2}P$
• D. $-2\sqrt{2}P$

Answer 1

The correct option is A $2\sqrt{2}P$

The resultant of 4 vectors in X, Y direction are:

resultant in X direction is

$3\overrightarrow{P}-\overrightarrow{P}=2\overrightarrow{P}$ (in -ve x direction)

In y direction is

$4\overrightarrow{P}-2\overrightarrow{P}=2\overrightarrow{P}$ (in +ve y direction)

So, the net resultant force vector is

$\overrightarrow{R}=2\overrightarrow{P}+2\overrightarrow{P}$

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.