Write the relation between angular momentum and rotational kinetic energy. For two objects of same angular momentum, compare the moment of inertia using the graph.

Explanation

Angular momentum, `L = I omega`
Rotational K.E., `E_(K) = (1)/(2) omega^(2)`
Multiply by 2I both sides (2I) `E_(K) = (cancel(2)I(I omega^(2)))/(cancel(2))`
2I `E_(k) = (Iomega)^(2)`
`E_(k) = ((I omega)^(2))/(2I)" "[because L = I omega]`
`E_(k) = (L^(2))/(2I)`
Where, L is the angular momentum and I is the moment of inertia.
Graph between KE and L :

The graph shows that of the two bodies of same angular momentum, those one have less rotational kinetic energy has higher moment of inertia.