First slide

Scalars and Vectors

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

Moderate

A

6N and 10N
B

8N and 8N
C

4N and 12N
D

2N and 14N

Solution

Let say A is the smaller force.
$\begin{array}{l} A + B = 16 (given) ........(i) \\ \tan ϕ = \frac{B \sin θ}{A + B \cos θ} = \tan 90^{\circ} \\ ∴ A + B \cos θ = 0 \Rightarrow \cos θ = \frac{- A}{B} . . . . . . . . (i i) \\ 8 = \sqrt{A^{2} + B^{2} + 2 A B \cos θ} . . . . . . . . (i i i) \end{array}$
By solving eqs (i), (ii) and (iii) we get A = 6 N, B = 10 N

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