Two parallel forces P and Q (P gt Q) are acting at two points, A and B, of a body. If the forces interchange their positions, by how much will the point of action of the resultant of the resultant of the two forces shift along the line AB?

Two parallel forces P and Q (P gt Q) are acting at two points, A and B

1.	Two parallel forces P and Q (P gt Q) are acting at two points, A and B, of a body. If the forces interchange their positions, by how much will the point of action of the resultant of the resultant of the two forces shift along the line AB?
Answer» Solution :In Fig. SUPPOSE C is the point of ACTION of the resultant in the first case. `:. PxxAC=QxxBC""cdots(1)` If the NEW POSITION of the point of action of the resultant is C. then `QxxAC.=PxxBC. ""cdots(2)` From (1) we get, `PxxAC = Q(AB-AC) " ""or", (P+Q)xxAC=QxxAB` `:. AC=(Q)/(P+Q)xxAB` Similarly from (2) we get, `AC.=(P)/(P+Q)xxAB ""cdots(4)` `:.` Subtracting equation (3) from equation (4) we get, `AC. -AC =(AB)/((P+Q))(P-Q) " ""or", "CC".= (P-Q)/(P+Q) xxAB`.