Question

A deformable body is under the action of external forces (F_i). The external forces satisfy the following conditions with respect to an inertial frame :

(i) ∑F_i = 0

(ii) ∑r_i × F_i = 0

These conditions are:

1. necessary and not sufficient for equilibrium
2. sufficient for equilibrium
3. necessary and sufficient for equilibrium
4. None of the above

Answer 1

Correct Answer - Option 1 : necessary and not sufficient for equilibrium

Explanation:

Equilibrium conditions for deformable bodies:

A system in which all the forces act in the same plane is termed a coplanar force system.

For any system of coplanar forces to be in equilibrium following conditions should be satisfied:

• The algebraic sum of the horizontal components of all the forces should be zero.
• The algebraic sum of the vertical components of all the forces should be zero.
• The algebraic sum of moments of all the forces about any point should be zero.

ΣFx = 0, ΣFy = 0 and ΣM = 0

Here, Only two conditions are given in the question.

Hence, Given conditions are necessary but not sufficient for equilibrium.