Question 21: Laws of Motion

Question

A body initially at rest undergoes rectilinear motion. The forcetime (F-t) graph for the motion of the body is given below. Find the linear momentum gained by the body in $2 \mathrm{~s}$.
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Accepted Answer

The correct answer is
Option B: Though they are equal in magnitude and opposite in direction they act on different bodies.
According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. This can be stated mathematically as:
$ \vec{F}_{	ext{action}} = -\vec{F}_{	ext{reaction}} $
Here, the action force and the reaction force are equal in magnitude but opposite in direction. However, the crucial detail is that these forces act on different bodies. This means that they do not cancel each other out since they do not act on the same object. As a result, the forces create effects on their respective objects rather than balancing each other out.
Let's consider an example to illustrate this concept. Imagine you push against a wall with a force of 50 N. According to Newton's Third Law, the wall pushes back against you with an equal and opposite force of 50 N. While these forces are equal in magnitude and opposite in direction, the action force is exerted on the wall, and the reaction force is exerted on you. Hence, they act on different bodies and do not cancel each other out.
This clearly demonstrates why action and reaction forces can never balance out despite being equal and opposite. The key point is that they act on different objects, causing them to produce effects on those objects independently.

Answer

$
\pi N-s
$

Answer

$
\frac{\pi}{2} \mathrm{~N}-\mathrm{s}
$

Answer

$
\frac{\pi}{4} N-s
$

Answer

$
2 \pi N-s
$

Laws of Motion

A body initially at rest undergoes rectilinear motion. The forcetime (F-t) graph for the motion of the body is given below. Find the linear momentum gained by the body in 2 \mathrm{~s}.

Choose the correct answer: