Question

Two forces 5 and 10 kg wt are acting with an inclination of 120o between them. What is the angle which the resultant makes with 10kg wt?

CLASS - XI PHYSICS (Kinematics)

Answer 1

Let P = 5 kg weight = 5 g Newtons
Q = 10 g Newtons

Using the parallelogram law of addition of vectors :
Resultant force magnitude = R
   R² = P² + Q² + 2 P Q Cos Ф = 5² + 10² + 2 * 5 * 10 * Cos 120
       = 125 - 50 = 75
R = 5√3 newtons

Angle made by R with Q = 10 kg weight = α 
         tan α = P Sin Ф / ( P + Q Cos Ф)
                 = 5 Sin 120 / (10 + 5 Cos 120) = 2.5 √3 / 7.5 = 1/√3
            α = 30°

Answer 2

Answer:

Let W1=5

W2=10

Q(angle)=120⁰

Tan (alpha)=BsinQ/A+BcosQ

Tan(alpha)=5×sin120⁰/5+10cos120⁰

Tan(alpha)=1/√3

alpha=30⁰