\[\begin {array} {1 1} (a)\;5:2 & \quad (b)\;1:1 \\ (c)\;2:3 & \quad (d)\;3:2 \end {array}\]

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Since the collision in elastic, and head on between the two identical masses, they interchange their linear velocities.

Since no tangential forces are presents, the angular velocity of ball A is not affected.

hence body A has pure rotational with angular velocity w and body B has pure translation with linear velocity V.

$\large\frac{KE_A}{KE_B}$ after collision = $\large\frac{1/2 I w^2}{1/2 I wV^2}$

$\qquad= \large\frac{\Large\frac{1}{2} \frac{2}{3}mR^2w^2}{\frac{1}{2} m V_0^2}$

$\qquad= \large\frac{2}{3}$$\qquad $$[Since\; V_0=Rw]$

Hence d is the correct answer

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