Answer
(2) is greatest, then (1) and (3) tie.
Work Step by Step
We were given the rest energy and total energy, respectively ,of three particles, expressed in terms
of a basic amount A as (1) A, 2A; (2) A, 3A; (3) 3A, 4A.
Without calculations, we want to rank them according to their kinetic energy; greatest first.
The total energy, E, is the sum of the rest energy, $mc^2$, and kinetic energy, K. And we can arrange it to isolate K.
$$E = mc^2 + K $$
$$K=E-mc^2 $$
We can see that the kinetic energy is based on the difference of the total energy and the rest energy.
Particle (2) has the largest differnce at 2A. Particles (1) and (3) both have a difference of "A" and so they have the same kinetic energy and are both less than (2).
