Hello Aspirant,

Given - Translational K.E of rolling sphere                = (1/2) × m × v^2.

= 5 J

So, mv^2 = 10.       ----------[Eqn- 1]

To find - Translational K.E

Solution- We know that v = r × ω.

Rotational K.E = (1/2) × I × ω^ 2.

We know that I = (2/5) × m × r ^2.

Hence,

Rotational K.E = (1/2) × (2/5) × m × r ^2 × ω^ 2

= (1/5) × m × r ^2 × ω^ 2

= (1/5) × m× v^2 = (1/5) × 10

----[from Eqn-1]

= 2 J.

I hope it helps

Thank you.