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 .

Step-by-step solution

Let A and B be 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 A B c o s θ ⇒ 28 = 3 x 2 + 5 x 2 + 2 3 x 5 x c o s 60 ° = 9 x 2 + 25 x 2 + 15 x 2 = 7 x ⇒ x = 28 7 = 4 Hence, force B = 5 × 4 = 20 N