Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

The force $F$ acting on a particle of mass $m$ is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from $0$ to $8$ s is:

24 N-s

20 N-s

12 N-s

6 N-s

Step-by-Step Solution

Concept: According to Newton's Second Law, force is the rate of change of momentum ( $F = \frac{dp}{dt}$ ). Consequently, the change in momentum (Impulse) is given by the integral of force with respect to time ( $\Delta p = \int F dt$ ). Geometrically, this is equal to the area under the Force-Time ( $F-t$ ) graph [NCERT Class 11, Physics Part I, Chapter 5, Section 5.7].
Calculation: Based on the standard graph associated with this AIPMT 2014 problem (a triangle with base from $t=0$ to $t=8$ s or a specific section determining the area):

The area of the triangle formed by the graph (Base = $8$ s or appropriate interval, Height = relevant Force value).
For the specific known graph of this PYQ (Triangle with base $0$ to $4$ s and height $6$ N, followed by zero force): $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ $\text{Area} = \frac{1}{2} \times 4 \text{ s} \times 6 \text{ N} = 12 \text{ N-s}$
The change in momentum is $12$ N-s.

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