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Difficulty: MediumNewton's Laws of Motion and Linear Momentum

When a constant net external force is applied to a body for a given time interval, the magnitude of the change in the body's linear momentum depends only on the magnitude of the applied force and the time duration, and is completely independent of the mass of the body.

Answer: Answer

Answer

The statement is True. By the impulse-momentum theorem (Δp=FΔt\Delta p = F \Delta t), the change in linear momentum is equal to the applied impulse, which depends only on force magnitude and time duration, regardless of the body's mass.
The statement is correct because impulse is defined as the product of net force and time interval (J=FΔtJ = F \Delta t), and by the impulse-momentum theorem, impulse equals the change in momentum (Δp=J\Delta p = J). Neither net force nor time interval depends on the mass of the body.

Step-by-Step Solution

1
Express Newton's Second Law of Motion in terms of linear momentum.
F=ΔpΔtF = \frac{\Delta p}{\Delta t}, where FF is the net force and Δp\Delta p is the change in linear momentum over time Δt\Delta t.
Newton's second law states that the net force acting on an object equals the rate of change of its linear momentum.
2
Rearrange the equation to isolate the change in momentum (Δp\Delta p).
Δp=FΔt\Delta p = F \Delta t.
Multiplying both sides by Δt\Delta t gives the impulse-momentum relationship.
3
Evaluate the dependence of Δp\Delta p on the body's mass.
The expression Δp=FΔt\Delta p = F \Delta t contains only force and time, with no mass term (mm).
Although a heavier body experiences smaller acceleration than a lighter body under the same force, both undergo the exact same total change in linear momentum over identical time intervals.

Key Concept

Impulse-Momentum Theorem and Newton's Second Law
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Topics

Newton's Laws of Motion and Linear Momentum

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