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(B) For a rigid diatomic molecule,the degrees of freedom $(f_A)$ are $5$ ($3$ translational + $2$ rotational).For a diatomic molecule with an addition

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$5:7$

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(B) For a rigid diatomic molecule,the degrees of freedom $(f_A)$ are $5$ ($3$ translational + $2$ rotational).For a diatomic molecule with an additional vibrational mode,the degrees of freedom $(f_B)$ are $7$ ($3$ translational + $2$ rotational + $2$ vibrational).The molar specific heat at constant volume is given by $C_v = \frac{f}{2}R$.Therefore,$C_v^A = \frac{5}{2}R$ and $C_v^B = \frac{7}{2}R$.The ratio $\frac{C_v^A}{C_v^B} = \frac{\frac{5}{2}R}{\frac{7}{2}R} = \frac{5}{7}$.

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