Question

If P is the force acting on the body, m is the mass of the body and a is the acceleration of the body, then according to Newton's second law of motion: ____.

• A. P + m.a = 0
• B. P - m.a = 0
• C. P × m.a = 0
• D. P m.a = 0

Hint:

Think of $P = ma$ as the "active" form of the law and $P - ma = 0$ as the "equilibrium" form. Both describe the same physical reality: force and mass-acceleration are always perfectly balanced.

Answer 1

The Correct Option is B

Step 1: D'Alembert's principle treats the mass's resistance to acceleration as an equivalent inertial force of magnitude \( ma \), acting opposite to the direction of the real applied force.

Step 2: Under this view, a body under an applied force \( P \) is treated as being in equilibrium once the fictitious inertial force \( -ma \) is included alongside the real force: \[ P + (-ma) = 0 \]

Step 3: Simplifying the expression gives the same relation as Newton's second law, just rearranged into an equilibrium form: \[ P - ma = 0 \] \[ \boxed{P - m \cdot a = 0} \]