Test: Equilibrium of a Particle (NCERT) - NEET MCQ

For equilibnum under the effect of the three cuncurrent force all the properties mentioned are required.

If 1 N and 2 N act in same direction and 3 N acts in opposite direction, then equilibrium is possible.

Applying equilibrium conditions, ∑F_x = 0
⇒ F₁ + 1sin45^∘ − 2sin45^∘ = 0
or F₁ = 2sin45^∘ − 1sin45^∘
= 
and ∑F_y= 0
⇒ 1cos45^∘ + 2cos45^∘− F₂ = 0
F₂ = 

Here, m = 10 kg
The resultant force acting on the body is
F = √(8N)² + (6N)² = 10N
Let the resultant force F makes an angle θ w.r.t. 8N force.
From figure, tanθ = 6N/8N = 3/4
The resultant acceleration of the body is

The resulatnt acceleration is along the direction of the resulatnt force.

Hence, the resultant acceleration of the body is 1 ms⁻² at an angle of tan⁻¹(3/4) w.r.t. 8N force.

For uniform velocity, acceleration is zero. Hence resultant force will be zero
∴   = 0