The angular momentum of a rigid body of mass m  about an axis is n times the linear momentum (P) of the body. Total kinetic energy of the rigid body is:

$$\begin{gathered} \mathrm{L} = \mathrm{nP} \\ \mathrm{KE} = {\mathrm{KE}}_{\mathrm{R}} + {\mathrm{KE}}_{\mathrm{T}} \end{gathered}$$

        $\begin{array}{l}=\frac{{\mathrm{L}}^2}{2\mathrm{I}}+\frac{{\mathrm{P}}^2}{2\mathrm{m}}\\ =\frac{{\mathrm{n}}^2{\mathrm{P}}^2}{2\mathrm{I}}+\frac{{\mathrm{P}}^2}{2\mathrm{m}}\\ =\frac{{\mathrm{P}}^2}{2}\left(\frac{{\mathrm{n}}^2}{\mathrm{I}}+\frac{1}{\mathrm{m}}\right)\end{array}$

NOTE: According to the solution None of the options were matching in the original question. Here we changed the option 1 for the conevenience of the student.