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: Understanding the Concept:
Newton's Second Law defines the relationship between force, mass, and acceleration, stating that the force applied to an object is equal to the rate of change of its momentum.

Step 2: Key Formula or Approach:
The standard mathematical form is: \[ P = m \cdot a \]

Step 3: Detailed Explanation:
The law states that the net force ($P$) acting on a body is the product of its mass ($m$) and its acceleration ($a$). To express this as an equation equal to zero (often used in D'Alembert's principle where $-ma$ is considered an inertial force): \[ P = m \cdot a \] Subtracting $m \cdot a$ from both sides: \[ P - m \cdot a = 0 \] This shows the balance between the applied force and the inertial resistance of the body.

Step 4: Final Answer:
According to the law, the correct relation is P - m.a = 0.

Answer 2

Newton's second law states \( P = m \cdot a \), relating force, mass and acceleration. We can check which rearrangement of this relation is algebraically consistent by testing each option directly against \( P = ma \).

1. \( P + m.a = 0 \): Rearranging gives \( P = -ma \), meaning the force would always have to be exactly opposite in sign to \( ma \). Since \( P = ma \) is the actual law, same sign, not opposite, this option contradicts the basic relation and is incorrect.
2. \( P - m.a = 0 \): Rearranging gives \( P = ma \), which is exactly Newton's second law itself, just written so that it equals zero. This is a direct, valid restatement of the law.
3. \( P \times m.a = 0 \): This equation would only be true if either \( P = 0 \) or \( ma = 0 \), since a product is zero only when at least one factor is zero. That would mean either no force or no acceleration at all times, which is not what the second law states in general, so this option is incorrect.
4. \( P\ m.a = 0 \): Read as a product of \( P \) and \( ma \), this suffers exactly the same flaw as the previous option: it would force either the applied force or the acceleration to always be zero, which is not the general statement of the second law.

Only rearranging \( P = ma \) to \( P - ma = 0 \) preserves the actual physical content of the second law.

Therefore, the correct answer is P - m.a = 0.