The sum of the magnitudes of two forces acting at a 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?

Options

A. 12,5
B. 14,4
C. 5,13
D. 10,8

Answer

C

Explanation

Let `P` be the smaller force and `Q` be the greater force then according to problem
`P+Q= 18`….(i)
`R= sqrt(P^(2)+Q^(2)+2PQ cos theta)=12`
`tan phi = (Q sin theta)/(P+Qcos theta)= tan 90^(@)= oo`
`:. P+Q cos theta= 0` (iii)
By solving (i),(ii) and (iii) we will get `P=5 and Q= 13`