A metallic rod of length $1 \, \text{m}$, held along the east-west direction, is allowed to fall freely. Given the horizontal component of Earth's magnetic field $B_{H} = 3 \times 10^{-5} \, \text{T}$, the emf induced in the rod at an instant $t = 2 \, \text{s}$ after it is released is (Take $g = 10 \, \text{m/s}^{2}$)?