Question

Condition of static equilibrium of a planar force system is written as
1. ΣF = 0
2. ΣM = 0
3. ΣF = 0 and ΣM = 0
4. None of these

Answer 1

Correct Answer - Option 3 : ΣF = 0 and ΣM = 0

Explanation:

Equilibrium of planar forces:

If the forces acting on the free-body are non-concurrent then the equivalent resultant will be a single force acting at a common point and a moment about the same point. The effect of such a force system will be to translate the body as well as to rotate it. Hence, for equilibrium to exist, both the force and moment must be null vectors.

i.e ΣF = 0, ΣM = 0

When the forces acting on a body lie in a plane (X - Y plane) but are non-concurrent, the body will have rotational motion perpendicular to the plane in addition to the translational motion along the plane, Hence necessary and sufficient condition for static equilibrium are,

ΣF_x = 0, ΣF_y = 0, ΣM_z = 0