Question

Two forces are such that the sum of their magnitudes is 18 N and their resultant is perpendicular to the smaller force and magnitude of resultant is 12. Then the magnitudes of the forces are

• A. 12 N, 6 N
• B. 1 N, 5N
• C. 10 N, 8 N
• D. 16 N, 2 N

Answer 1

Answer: (B)

1 N, 5N

Answer 2

Let two forces are $F_{1}$and $F_{2}(F_{1} < F_{2})$.

According to problem: $F_{1} + F_{2} = 18$ …..(i)

Angle between $F_{1}$and resultant (R) is 90⁰

$\therefore$ $\tan 90 = \frac{F_{2}\sin\theta}{F_{1} + F_{2}\cos\theta} = \infty$

$\Rightarrow F_{1} + F_{2}\cos\theta = 0$

⇒ $\cos\theta = - \frac{F_{1}}{F_{2}}$ …..(ii)

and $R^{2} = F_{1}^{2} + F_{2}^{2} + 2F_{1}F_{2}\cos\theta$

$144 = F_{1}^{2} + F_{2}^{2} + 2F_{1}F_{2}\cos\theta$ …..(iii)

by solving (i), (ii) and (iii) we get $F_{1} = 5N$and $F_{2} = 13N$