Q54 / 270 · NDA 2025 (Phase 2) · General Ability
Which one of the following statements for second law of motion is NOT correct?
- AThe net force on a body is proportional to that body's acceleration
- BThe net force on a body is in the same direction as the acceleration
- CThe time rate of change of momentum is equal to force
- Correct answerDThe net force on a body is proportional to that body's momentum
Solution
According to Newton's second law of motion, the rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts.
Mathematically, $\vec{F} = \dfrac{d\vec{p}}{dt}$.
For a body of constant mass, $\vec{F} = m\vec{a}$. This implies that the net force is proportional to the acceleration and acts in the same direction as the acceleration.
The net force is proportional to the time rate of change of momentum, not to the momentum itself. Therefore, the statement that the net force on a body is proportional to that body's momentum is incorrect.
Answer: The net force on a body is proportional to that body's momentum
Mathematically, $\vec{F} = \dfrac{d\vec{p}}{dt}$.
For a body of constant mass, $\vec{F} = m\vec{a}$. This implies that the net force is proportional to the acceleration and acts in the same direction as the acceleration.
The net force is proportional to the time rate of change of momentum, not to the momentum itself. Therefore, the statement that the net force on a body is proportional to that body's momentum is incorrect.
Answer: The net force on a body is proportional to that body's momentum
Hence, the correct answer is option: 'D'.