Question

Which of the following statements correctly explains the relationship between force and momentum?

• A. The rate of change of momentum of a body is directly proportional to the applied force and occurs in the direction of the force.
• B. The rate of change of momentum of a body is inversely proportional to the applied force and always oppose the direction of the force.
• C. The rate of change of momentum of a body is proportional to the square of the applied force and takes place in the direction opposite to the force.
• D. The rate of change of momentum of a body is independent of the applied force but depends on the direction of motion of the body.

Hint:

Newton's Second Law is often simplified to \( F = ma \), but its more fundamental and complete definition is in terms of momentum: Force is the rate of change of momentum (\( F = \frac{\Delta p}{\Delta t} \)).

Answer 1

The Correct Option is A

This question describes Newton's Second Law of Motion.
Step 1: State Newton's Second Law. Newton's Second Law states that the net force acting on an object is equal to the rate at which its momentum changes. Mathematically, this is expressed as \( F = \frac{dp}{dt} \), where \( F \) is the force, \( p \) is the momentum, and \( t \) is time.

Step 2: Analyze the relationship. The formula \( F = \frac{dp}{dt} \) shows that the force (\(F\)) is directly proportional to the rate of change of momentum (\(\frac{dp}{dt}\)). Force and momentum are vector quantities, and the law specifies that the change in momentum occurs in the same direction as the applied net force.

Step 3: Evaluate the options.
- Option (1) correctly states this relationship: "directly proportional to the applied force and occurs in the direction of the force."
- Option (2), (3), and (4) state incorrect relationships (inversely proportional, proportional to the square, independent).
Therefore, option (1) is the correct statement of the law.