The ratio of kinetic energies of $1\mathrm{g}$ of ${\mathrm{H}}_2$ $2\mathrm{g}$ of ${\mathrm{CH}}_4$ at the same temperature will be

We know that

The kinetic energy of a gas molecule is independent of its molar mass and at constant temperature, the kinetic energy of a gas molecule is constant.

Therefore, the ratio of kinetic energy of 1 $\mathrm{g}$ of ${\mathrm{H}}_2$ and $2 \mathrm{g}$ of ${\mathrm{CH}}_4$ at the same temperature will be equal to the ratio of their number of moles. 

Now, the number of moles of hydrogen are $\frac{1 \mathrm{g}}{2 \mathrm{g}/\mathrm{mol}}=0.5 \mathrm{mol}$

And the number of moles of methane are $\frac{2 \mathrm{g}}{16 \mathrm{g}/\mathrm{mol}}=0.125 \mathrm{mol}$

Then, the ratio of the number of moles of hydrogen to the number of moles of methane are

$\frac{0.5}{0.125}=4:1$

Hence, the ratio of kinetic energy of $1 \mathrm{g}$ of ${\mathrm{H}}_2$ and $2 \mathrm{g}$ of ${\mathrm{CH}}_4$ at the same temperature will be 4: 1.

Therefore, option(B) is the answer.