Two forces of magnitudes 8 N and 15 N respectively act at a point so as to make the resultant force of 17 N. The angle between the forces has to be

Question

Two forces of magnitudes 8 N and 15 N respectively act at a point so as to make the resultant force of 17 N. The angle between the forces has to be (A)  45°  (B)  60°  (C)  90°  (D)  120°

Tardigrade Admin · Accepted Answer

: Resultant force =17 text N ∴ R2-P2+Q2+2PQcosθ or (17)2=(8)2+(15)2+2.PQcosθ or 289=64+225+2PQcosθ or cos θ =0 or θ =90°

Q. Two forces of magnitudes 8 N and 15 N respectively act at a point so as to make the resultant force of 17 N. The angle between the forces has to be

$45^{\circ}$

$60^{\circ}$

$90^{\circ}$

$120^{\circ}$

: Resultant force $= 17 N$ $∴$ $R^{2} - P^{2} + Q^{2} + 2 PQ cos θ$ or $(17)^{2} = (8)^{2} + (15)^{2} + 2. PQ cos θ$ or $289 = 64 + 225 + 2 PQ cos θ$ or $cos θ = 0$ or $θ = 90^{\circ}$