State the principle of virtual work.

• A. The sum of kinetic energies is minimized
• B. For a system in equilibrium, the total virtual work of real forces during any virtual displacement is zero
• C. The total real work done is maximum
• D. Virtual work equals zero only for conservative forces

Answer: (B)

In equilibrium, any tiny imaginary move you imagine for the system that respects the constraints should not cause the real forces to do net work. Put simply, the total virtual work done by the real forces during such a virtual displacement is zero. Mathematically, for any admissible virtual displacement δr, the sum of Fi · δri over all real forces Fi equals zero. This must hold for all virtual displacements allowed by the constraints, which is what makes the principle so powerful for finding equilibrium conditions without tracking actual motion.

This isn’t about minimizing kinetic energy or maximizing real work. It also isn’t limited to conservative forces; the zero virtual-work condition applies to the real forces present, provided the system is in equilibrium and the displacements are compatible with the constraints.