The necessary condition of equilibrium of a body is-

The necessary conditions for a body to be in equilibrium are that both the sum of all forces and the sum of all moments acting on the body must equal zero. Here's the breakdown:

Key Analysis of Options:
1. Option 1 (∑Fy = 0, ∑M = 0)
   Missing ∑Fx = 0. If horizontal forces are unbalanced, the body will accelerate horizontally, violating equilibrium.

2. Option 2 (∑Fx = 0, ∑M = 0)
   Missing ∑Fy = 0. Unbalanced vertical forces would cause vertical acceleration.

3. Option 3 (∑Fx = 0, ∑Fy = 0)
   Missing ∑M = 0. Even if forces balance, unbalanced moments will cause rotation.

4. Option 4 (∑Fx = 0, ∑Fy = 0, ∑M = 0)
   Correct. For equilibrium:  
   - Translational equilibrium: All forces must cancel (∑Fx = 0, ∑Fy = 0).  
   - Rotational equilibrium: All moments (torques) must cancel (∑M = 0).  

Why Option 4 is Necessary:
- Forces and moments are independent conditions. Even if forces balance, moments can still cause rotation (e.g., a couple force-pair).  
- All three conditions must be satisfied simultaneously for complete static equilibrium