Two forces whose magnitude are in the ratio 9:11 give a resultant of 38 N. If the angle of their inclination is 30° then what will be the magnitude of each force?

Question

Two forces whose magnitude are in the ratio 9:11 give a resultant of 38 N. If the angle of their inclination is 30° then what will be the magnitude of each force? (A) 19.8 N, 24.2 N (B) 20N, 24 N (C) 25 N, 30 N (D) None of these

Tardigrade Admin · Accepted Answer

Let the two forces A and B A=9 x, B=11 x θ=30 ∴ (A/B)=(9/11) R=√A2+B2+2 A B cos θ 38=√(9 x)2+(11 x)2+2 × 9 x × 11 x × (1/2) 38=√81 x2+121 x2+99 x2 38=√301 x 2 38=17.3 x ⇒ x=(38/17.34)=2.19 ≈ 2.2 Thus = A =9 × x =9 × 2.2=19.8 N B=11 x=11 × 2.2=24.2 N

Q. Two forces whose magnitude are in the ratio $9 : 11$ give a resultant of $38$ N. If the angle of their inclination is $3 0^{\circ}$ then what will be the magnitude of each force?

$19.8 N, 24.2 N$

$20 N, 24 N$

$25 N, 30 N$

None of these

Q. Two forces whose magnitude are in the ratio 9:11 give a resultant of 38 N. If the angle of their inclination is 30∘ then what will be the magnitude of each force?

19.8N,24.2N

20N,24N

25N,30N

None of these

Let the two forces A and B A=9x,B=11xθ=30 ∴BA​=119​ R=A2+B2+2ABcosθ​ 38=(9x)2+(11x)2+2×9x×11x×21​​ 38=81x2+121x2+99x2​ 38=301x2​ 38=17.3x⇒x=17.3438​=2.19≈2.2 Thus =A=9×x=9×2.2=19.8N B=11x=11×2.2=24.2N

Q. Two forces whose magnitude are in the ratio $9 : 11$ give a resultant of $38$ N. If the angle of their inclination is $3 0^{\circ}$ then what will be the magnitude of each force?

$19.8 N, 24.2 N$

$20 N, 24 N$

$25 N, 30 N$