Question

The sum of two forces acting at a point is 16 N. If the resultant force is 8 N and its direction is perpendicular to minimum force then the forces are

• A. 6 N and 10 N
• B. 8 N and 8 N
• C. 4 N and 12 N
• D. 2 N and 14 N

Answer 1

The correct option is A

6 N and 10 N

A+B=16 (given) .....(i)
$tan\alpha =\frac{Bsin\theta }{A+Bcos\theta }=tan{90}^{\circ }\therefore A+Bcos\theta 0\Rightarrow cos\theta =\frac{-A}{B}....\left(ii\right)S=\sqrt{A^2+B^2+2ABcos\theta }...\left(iii\right)$
By solving eq. (i), (ii) and (iii) we get A =6 N, B=10N