Question

For a body to be in equilibrium under concurrent coplanar forces, the sum of:

• A. Moments must be zero
• B. Forces in vertical direction must be zero
• C. All forces must be zero
• D. Horizontal and vertical components of forces must each be zero

Hint:

For a body to be in equilibrium under coplanar forces, both the horizontal and vertical components of the forces must balance out to zero. This ensures there is no translational movement in either direction.

Answer 1

The Correct Option is D

For a body to be in equilibrium under concurrent coplanar forces, there are two conditions that must be satisfied:
1. The sum of the forces in the horizontal direction must be zero.
2. The sum of the forces in the vertical direction must be zero.
These conditions ensure that the body does not experience any net force in either direction, meaning there is no translational motion. Additionally, for rotational equilibrium, the sum of the moments (torques) about any point must also be zero. However, the question specifically asks about the equilibrium of forces, not the moments.
Thus, the correct condition for equilibrium in the context of coplanar forces is that the horizontal and vertical components of the forces must each be zero. This guarantees that the body remains stationary with no net force acting on it in any direction.
Hence, the correct answer is: "Horizontal and vertical components of forces must each be zero."