Question

The law in which, the system of forces acting on a moving body is in dynamic equilibrium with the inertia force of the body is known as ............

• A. Lami’s theorem
• B. impulse momentum theorem
• C. work energy principle
• D. D’Alembert’s principle

Hint:

D'Alembert’s principle is widely used in dynamics, especially when dealing with moving bodies in equilibrium with both external forces and inertia forces.

Answer 1

The Correct Option is D

D'Alembert's principle is a fundamental principle of mechanics that allows us to analyze the motion of a body under the influence of forces and inertial forces. It is an extension of Newton's second law and is particularly useful in dynamic equilibrium problems where forces are in balance with the inertia force.
D'Alembert’s principle states that the sum of the applied forces and the inertial forces (fictitious forces) must be zero for a body in equilibrium. Mathematically, this can be expressed as: \[ \sum \vec{F} + \sum \vec{F_{\text{inertial}}} = 0 \] This principle allows us to solve dynamic problems in a similar way to static problems by transforming them into statics problems, where the system is in equilibrium.