Assertion and Reason on Newton’s Laws in Inertial Frames – Rankers Physics

Linear Momentum and Second Law of Motion: Practice Problem & Solution

A frame of reference A is moving rectilinearly and uniformly with a velocity \(\vec{u}\) with respect to an inertial frame B. A body is moving with velocity \(\vec{v}\) and acceleration \(\vec{a}\) in an inertial system B. Assertion (A): When we use Newtons second Law in frame B we write \( \Sigma \vec{F}_{net} = m\vec{a} \). Now when we use the same in frame A we will write exactly same \(\Sigma \vec{F}_{net}\) and \(\vec{a}\) . Reason (R): All inertial system are equally suitable for the description of physical phenomenon.
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Linear Momentum and Second Law of Motion. Understanding the underlying formula is key to arriving at the correct answer below:

Frame A, moving with constant velocity relative to inertial frame B, is also an inertial frame. Newton's second law \( \Sigma \vec{F}_{net} = m\vec{a} \) holds in all inertial frames with the same forces and acceleration. This is because all inertial systems are equally suitable for describing physical phenomena. Both A and R are true, and R explains A.

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