Two forces A and B whose magnitude are in the ratio 3: 5 give a resultant of 28 N. If the angle of their inclination is 60°, then the magnitude of force B will be N.

Question

Two forces A and B whose magnitude are in the ratio 3: 5 give a resultant of 28 N. If the angle of their inclination is 60°, then the magnitude of force B will be N. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Let A and B he the two forces. Then A =3 x ; B =5 x , R =28 N and θ=60° We know that R =√ A 2+ B 2+2 AB cos θ ⇒ 28=√(3 x)2+(5 x)2+2(3 x)(5 x) cos 60° =√9 x2+25 x2+15 x2=7 x ⇒ x=(28/7)=4 Hence, Force B=5 × 4=20 N

Q. Two forces A and B whose magnitude are in the ratio 3:5 give a resultant of 28N. If the angle of their inclination is 60∘, then the magnitude of force B will be______ N.

Let A and B he the two forces. Then A=3x;B=5x,R=28N and θ=60∘ We know that R=A2+B2+2ABcosθ​ ⇒28=(3x)2+(5x)2+2(3x)(5x)cos60∘​ =9x2+25x2+15x2​=7x ⇒x=728​=4 Hence, Force B=5×4=20N

Q. Two forces $A$ and $B$ whose magnitude are in the ratio $3 : 5$ give a resultant of $28 N$ . If the angle of their inclination is $6 0^{\circ}$ , then the magnitude of force $B$ will be______ $N$ .