**Correct Option: A** ### Detailed Explanation To determine whether an object is in equilibrium when multiple forces are acting on it, we need to analyze the conditions that must be satisfied. Equilibrium in physics means that the object is either at rest or moving with a constant velocity, which implies that there is no net force acting on it. 1. **Understanding Forces in Equilibrium**: - For an object to be in equilibrium, the vector sum of all forces acting on it must be zero. This can be broken down into two components: the horizontal (x-direction) and vertical (y-direction) components. - Mathematically, this is expressed as: - \( \sum F_x = 0 \) (the sum of all forces in the x-direction must equal zero) - \( \sum F_y = 0 \) (the sum of all forces in the y-direction must equal zero) 2. **Why Option A is Correct**: - Option A states that the sum of the forces in the x-direction must equal zero, and the sum of the forces in the y-direction must equal zero. This is the fundamental condition for translational equilibrium. If both conditions are satisfied, the object will not accelerate in any direction, thus achieving equilibrium. 3. **Why Other Options are Incorrect**: - **Option B**: "The net force must be equal to the gravitational force acting on the object." - This statement is misleading. While the gravitational force is one of the forces acting on the object, for equilibrium, the net force must be zero, not equal to the gravitational force. The gravitational force can be balanced by other forces (like normal force, tension, etc.), but they do not need to be equal in magnitude; they just need to sum to zero. - **Option C**: "The object must be at rest; otherwise, it cannot be in equilibrium." - This option is incorrect because equilibrium does not require the object to be at rest. An object can be in dynamic equilibrium, moving at a constant velocity. The key point is that the net force must be zero, not that the object must be stationary. - **Option D**: "The forces must be equal in magnitude regardless of their direction." - This statement is also incorrect. Forces can be of different magnitudes as long as they balance each other out in terms of direction. For example, a 5 N force to the right and a 5 N force to the left will result in equilibrium, but they are not equal in terms of direction. The direction of the forces is crucial in determining their net effect. ### Summary of Key Points - For an object to be in equilibrium, the vector sum of all forces acting on it must be zero. - This requires that the sum of forces in both the x-direction and y-direction equals zero. - Equilibrium can occur whether the object is at rest or moving at a constant velocity. - Forces do not need to be equal in magnitude; they must balance out in terms of their vector sum. ### Revision Summary - **Equilibrium Condition**: \( \sum F_x = 0 \) and \( \sum F_y = 0 \). - **Dynamic Equilibrium**: An object can be moving at constant velocity and still be in equilibrium. - **Force Direction Matters**: Forces can be unequal in magnitude but must balance out directionally. - **Gravitational Force**: It is one of the forces but does not dictate the net force condition for equilibrium.