In the arrangement shown in figure, if the system is in equilibrium, find tension   $T_1\left(inN\right)$ $(g=10m/s^2)$

Tension in Equilibrium

Given:

Equilibrium conditions:

300 sin(90° + θ) = T₁ sin 90° = 400 sin(180° - θ)

Step 1: Resolve components

Horizontal and vertical components:

300 cos θ = T₁ = 400 sin θ

Step 2: Find θ

tan θ = 400 / 300 = 4 / 3

θ = 53°

Step 3: Find tension T₁

T₁ = 400 sin θ

T₁ = 400 × sin 53° ≈ 500 N

OR 

Answer: The tension in the string is T₁ = 500 N.