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 then it is given that
`P+Q=18 " "` .............(1)
`R=sqrt(P^(2)+Q^(2)+2PQcos theta )=12" "` ..........(2)
`Q sin theta//P+Qcos theta=tanphi =tan90^(@)=infty`
`P+Q cos theta=0 " "` .......(3)
Substituting the value of P
`Q(1-cos theta) = 18 " "` .........(4)
and Subtracting square of equation (2) from (1)
`2PQ[1-cos theta]=18^(2)-12^(2)=180 " "` ..........(5)
Dividing equation (5) by (4)
`2P=10 i.e.P=5, "so" Q=13`
So the magnitude of forces are (5 and 13)
Hence correct answer is (c)