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Question

The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. If the resultant is at 90 with the force of smaller magnitude, what are the, magnitudes of forces  
  1. 12, 5    
  2. 14, 4
  3. 5, 13 
  4. 10, 8


Solution

The correct option is C 5, 13 

Let P be the smaller force and Q be the greater force then according to problem-
P + Q = 18 ..(i)
R = P2+Q2+2PQcosθ = 12 ..(ii)
tan ϕ = QsinθP+Qcosθ = tan 90 =
P + Q cos θ = 0 ..(iii)
By solving (i), (ii) and (iii) we will get P = 5 , and Q = 13

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