Not an original one

For this question we need to calculate the angular velocity and velocity of the combined mass after collision.

For velocity simply conserve momentum in horizontal direction-

$mv = 2mv^{\prime}$ , where $v^{\prime}$ is the velocity of the combined system.

Now to find the angular velocity , we will conserve angular momentum along the center of mass on the combined system . This is necessary as the combined body rotates along its c.o.m.

The center of mass of combined body lies on distance of $\dfrac R2$ from the c.o.m of each disc and at a distance of $R$ from c.o.m of disc as shown in figure:

Now first we need to find moment of inertia along the axis of c.o.m of combined body

$I = 2\times(MR^2 + \dfrac{MR^2}{2}) = 3MR^2$

Now from conservation of angular momentum:

$\dfrac{MVR}{2} = 3MR^2 \times \omega$

$\rightarrow \omega = \dfrac{V}{6R}$

Now to total energy of system is kinetic energy + rotational kinetic energy

$= \dfrac 12 MV^2 + \dfrac 12 I (\omega)^2$

Now just plug in the values to get amswer which is $\boxed{63}$