Answer
We can rank the situations according to the rate at which energy is transferred from us to thermal energy of the loop:
$(1) \gt (2) \gt (4) \gt (3)$
Work Step by Step
We can assume that the resistance of the loop is proportional to the total length of the loop.
We can write a general expression for the power transferred to the loop:
$P = \frac{B^2~L^2~v^2}{R}$
We can write an expression for the power transferred to each loop:
(1) $P = \frac{B^2~(2L)^2~v^2}{6R} = \frac{2}{3}~\frac{B^2~L^2~v^2}{R}$
(2) $P = \frac{B^2~(2L)^2~v^2}{8R} = \frac{1}{2}~\frac{B^2~L^2~v^2}{R}$
(3) $P = \frac{B^2~L^2~v^2}{6R} = \frac{1}{6}~\frac{B^2~L^2~v^2}{R}$
(4) $P = \frac{B^2~L^2~v^2}{4R} = \frac{1}{4}~\frac{B^2~L^2~v^2}{R}$
We can rank the situations according to the rate at which energy is transferred from us to thermal energy of the loop:
$(1) \gt (2) \gt (4) \gt (3)$
