Relativistic particle motion (Question 1 (5+3=8 Marks)) — UPSC Physics Optional IFoS 2024 Paper I

Write down the expression for kinetic energy of a relativistic particle with rest mass m_0, moving with a speed v. (i) Show that the kinetic energy reduces to \frac{1}{2} m_0 v^2 in the non-relativistic limit. (ii) Find the first relativistic correction to the non-relativistic kinetic energy.