**Correct Option: B. The vector sum of the forces must equal zero.** ### Detailed Explanation: To understand why option B is the correct answer, we need to delve into the concept of equilibrium in physics. An object is said to be in equilibrium when the net force acting on it is zero. This means that all the forces acting on the object balance each other out perfectly. 1. **Understanding Forces**: - In this scenario, we have three forces acting on a point object with magnitudes of 5 N, 10 N, and 15 N. These forces can be represented as vectors, which have both magnitude and direction. - For the object to be in equilibrium, the vector sum of these forces must equal zero. This means that if we were to add these forces together, taking into account their directions, the result should be a net force of zero. 2. **Vector Sum**: - The vector sum of forces involves not just adding their magnitudes but also considering their directions. For example, if two forces are acting in opposite directions, they will partially or completely cancel each other out. - Mathematically, if we denote the forces as \( \vec{F_1} = 5 \, \text{N} \), \( \vec{F_2} = 10 \, \text{N} \), and \( \vec{F_3} = 15 \, \text{N} \), we need to find a combination of these forces such that: \[ \vec{F_1} + \vec{F_2} + \vec{F_3} = 0 \] - This can be achieved if the forces are arranged in such a way that they balance each other out. For instance, if \( \vec{F_1} \) and \( \vec{F_2} \) act in one direction, \( \vec{F_3} \) must act in the opposite direction with a magnitude that balances the sum of \( \vec{F_1} \) and \( \vec{F_2} \). 3. **Why Other Options Are Incorrect**: - **Option A: The net force must equal 5 N.** - This option is incorrect because for an object to be in equilibrium, the net force must be zero, not equal to any non-zero value like 5 N. A net force of 5 N would indicate that the object is accelerating in the direction of that force. - **Option C: The largest force must be equal to the smallest force.** - This option is also incorrect. The largest force does not need to equal the smallest force for equilibrium. In fact, in many cases, the forces can be of different magnitudes and still achieve equilibrium if they are balanced correctly in terms of direction. - **Option D: The forces must be perpendicular to each other.** - This option is misleading. While forces can be perpendicular and still result in equilibrium, it is not a requirement. Forces can be at any angle to each other, as long as their vector sum equals zero. For example, two forces of equal magnitude acting at an angle can still balance each other out. ### Summary of Key Points: - An object is in equilibrium when the net force acting on it is zero. - The vector sum of all forces must equal zero for equilibrium to be achieved. - The magnitudes and directions of the forces must be considered in the vector sum. - Other options do not satisfy the condition for equilibrium as they misinterpret the requirements. ### Revision Summary: - Equilibrium requires the net force to be zero. - The vector sum of forces must equal zero. - Magnitudes and directions of forces are crucial in determining equilibrium. - Misinterpretations of force relationships can lead to incorrect conclusions about equilibrium.