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

Options

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

Answer

C

Explanation

Let smaller force be `F_(1)`. Rsultant R of the forces is at `90^(@)` to AB.
`therefore R^(2)+F_(1)^(2)=F_(2)^(2)" in "DeltaABC`
or `(12)^(2)=F_(2)^(2)-F_(1)^(2)...(i)`
or `144=(F_(2)-F_(1))(F_(2)+F_(1))`
but `F_(1)+F_(2)=18N` (given) ...(ii)

`therefore F_(2)-F_(1)=(144)/(18)=8 ...(iii)`
From Eqs. (ii) and (iii), `F_(1)=5, F=13`
Hence, force are 5 N and 13 N.