Question

Three forces are applied to a square plate as shown in figure:

Find the modulus of the resultant force.

• A. $F_{res}=F$
• B. $F_{res}=2F$
• C. $F_{res}=4F$
• D. $F_{res}=-2F$

Answer 1

The correct option is B $F_{res}=2F$

$\overrightarrow{F_{res}}=F\hat{i}$ (at point B) $+F\hat{j}$ (at point A) $+F\sqrt{2}(cos45^0\hat{i}-sin45^0\hat{j})$ (at point F)

or,$\overrightarrow{F_{res}}=2F\hat{i}.$

Thus, magnitude $=2F$.