CBSE Class 11-science Answered

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 P² = Q² +R²

or P² - Q² = R²

or  (P+Q) (P - Q) = R²

or P -Q = R²/P+Q

that is, P- Q = 144/18 = 8 ...(2)

Adding (1) and (2) ,

2P = 26

or P = 13 N .

Then Q = 5 N.