Two forces A and B whose magnitude are in the ratio 3:5 give a resultant of 28 textN . 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 textN . 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 be the two forces. Then A=3x; B=5x, R=28N and θ =60° . We know that R=√A2 + B2 + 2 A B c o s θ ⇒ 28=√(3 x)2 + (5 x)2 + 2 (3 x) (5 x) c o s (60)° =√9 x2 + 25 x2 + 15 x2=7x ⇒ x=(28/7)=4 Hence, force B=5× 4=20 textN

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 be 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)cos(60)∘​ =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 ----- $N$ .