The sum of the magnitudes of two forces acting at a point is 18N and the magnitude of their resultant is 12N. If the resultant is at `90^(@)` with the smaller force, the magnitude of the forces in newton are.

Options

A. 6,12
B. 11,7
C. 5,13
D. 14,4

Answer

C

Explanation

From figure it is deduced that,
`R^(2)+O^(2) =Q^(2)`
`(12)^(2)=Q^(2)-P^(2).....(1) & P+Q=18N ........(2)`
`Q^(2)-P^(2)=(Q+P) (Q-P), Q-P= 8N`
By rearranging and substituting, we get
`Q=13 N, P=5 N`