# The sum of the magnitudes of two forces acting at a point is 18 and the magnitude of the resultant is 12. If the resultant is at 90o with the force of smaller magnitude, what are the magnitudes of the two forces?

Aman Bansal
592 Points
13 years ago

Dear Dennis,

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.

Best Of luck

Cracking IIT just got more exciting,It’s not just all about getting assistance from IITians, alongside Target Achievement and Rewards play an important role. ASKIITIANS has it all for you, wherein you get assistance only from IITians for your preparation and winexciting gifts by answering queries in the discussion forums. Reward points 5 + 15 for all those who upload their pic and download the ASKIITIANS Toolbar, just a simple click here to download the toolbar….
So start the brain storming…. become a leader with Elite Expert League ASKIITIANS

Thanks

Aman Bansal