Question

Three forces are applied to a square plate as shown in figure:
Find the point of application of the resultant force, if this point is taken on the side $BC$.

• A. The force is applied at the midpoint of the side $BC$.
• B. At point B
• C. At point C
• D. cannot be found

Answer 1

The correct option is A The force is applied at the midpoint of the side $BC$.

Since a vector can be translated parallely along its line of action, hence shift the force at D to A. Thus, Resultant of the forces at A and D is : $\overrightarrow{F_{Res}}=F\hat{j}+F\sqrt{2}(cos45^0\hat{i}-sin45^0\hat{j})$, which acts at point A and is parallel to diagonal AC. Resultant of this force and force at B, which is again in the same direction as this force, will also be along AC. Since these two forces are of equal magnitude F, thus their combined resultant will act at their centre point. Projecting this centre point of A and B along line BC, we get the mid point of BC. Thus resultant acts at mid of BC.