Two forces of magnitude 8 N and 15 N respectively act at a point. If the resultant force is 17 N, the angle between the forces has to be

Question

Two forces of magnitude 8 N and 15 N respectively act at a point. If the resultant force is 17 N, the angle between the forces has to be (A) 60° (B) 15° (C) 90° (D) 30°

Tardigrade Admin · Accepted Answer

R=√A2+B2+2 A B cos θ A=8, B=15, R=17 172=82+152+2 × 8 × 15 × cos θ 289=64+225+240 cos θ ⇒ 289=289+24 cos θ 24 cos θ=0 cos θ=0 ⇒ θ=90°

Q. Two forces of magnitude $8 N$ and $15 N$ respectively act at a point. If the resultant force is $17 N$ , the angle between the forces has to be

$6 0^{\circ}$

$1 5^{\circ}$

$9 0^{\circ}$

$3 0^{\circ}$

$R = A^{2} + B^{2} + 2 A B cos θ$
$A = 8, B = 15, R = 17$
$1 7^{2} = 8^{2} + 1 5^{2} + 2 \times 8 \times 15 \times cos θ$
$289 = 64 + 225 + 240 cos θ$
$\Rightarrow 289 = 289 + 24 cos θ$
$24 cos θ = 0$
$cos θ = 0 \Rightarrow θ = 9 0^{\circ}$

Q. Two forces of magnitude 8N and 15N respectively act at a point. If the resultant force is 17N, the angle between the forces has to be

60∘

15∘

90∘

30∘