Understanding the reasoning of this answer

[Abhishek11235]

Homework Statement

This is exercise from Morin's book of classical mechanics(Q-12.14 in screenshot 2). He asks to calculate force in 2 different frames. I got the answer and it matches with the solution provided(Screenshot 3). However,the forces in 2 frames must be equal since longitudinal components of force are same. Morin provides explanation for this paradox which completely goes over my understanding(Screenshot 1). Can anybody help me in understanding the reasoning of paradox?

Relevant Equations

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[kuruman]

Please be more considerate when seeking assistance. It would help us help you if you posted the actual statement of the problem, not your synopsis of it. For example, although I can guess that it involves a relativistic calculation and I understand what $\gamma$ stands for, I have no idea what $\sigma$ is all about and I don't want to guess how it is defined. It would also help to show the "above" as in "$\dots$we have seen above that it is $\gamma^2 \sigma v ...$"