Question

two forces are such that sum of the magnitude is 18N and magnitude of the resultant is 12N , which is perpendicular to the smaller force, then the magnitude of the forces are?

Answer 1

Let P and Q be the forces and P is greater than Q , acting at a point O inclined angle .Here P+Q = 18 ....(1) and the resultant  R =12 N.   Construct a parallelogram with sides with OA = Q, OB = P, with angle AOB as an obtuse angle and OA along the x axis.Draw the diagonal OC  to the parellelogram OACB  so that angle AOC =90 degree .The diagonal OC = resultant R which is perpendicular to the s maller force Q .  consider the triangle AOC , OA = P, AC = OB  = P, and angle AOC =90degree.That is triangle AOC is a right angled triangle with AC = P as hypotenuse. Then   P^ 2  = Q^2 +R^2  or P^2 - Q^2 = R^2  or (P+Q) (P - Q)  = R^2   or P -Q  = R^2/P+Q that is   P- Q  = 144/18   = 8  ...(2)    Adding (1) and (2)   2P = 26 or P = 13 N . Then Q = 5 N. I THINK U GOT IT!