One-dimensional Head-on Collision – Rankers Physics

Collision: Practice Problem & Solution

Consider a one-dimensional head on collision of two balls. Assertion (A): The loss in kinetic energy of the system during the collision does not depend on the velocity of the observer. Reason (R): Kinetic energy of a body is independent of velocity of observer.  
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Collision. Understanding the underlying formula is key to arriving at the correct answer below:

Assertion (A): The loss in kinetic energy of a system is generally dependent on the observer's frame of reference. Thus, (A) is false.

Reason (R): Kinetic energy \(K = \frac{1}{2}mv^2\) depends on the velocity (v\), which is relative to the observer. Therefore, kinetic energy is dependent on the velocity of the observer. Thus, (R) is false.

Since both (A) and (R) are false, option (4) is correct.

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