Question

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 $N$ are

• A. 6, 12
• B. 11, 7
• C. 5, 13
• D. 14, 4
• E. 10, 8

Answer 1

Answer: (C)

Let smaller force be $F_1$ .
Resultant R of the forces is at $90{}^{∘}$ to AB,
$∴R^2+F_1^2=F_2^2$ in $ΔABC$
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)
$∴$ $F_2−F_1=\frac{144}{18}=8$ ....(iii)
From Eqs. (ii) and (iii),
$F_1=5,F_2=13$
Hence, forces are 5 N and 13 N.