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

Let a rigid body of moment of inertial rotate with angular velocity `omega` .
The angular momentum of a rigid body is, `L= Iomega`.
The rotational kinetic energy of the rigid body is, `KE=(1)/(2)I omega^(2)`.
By multiplying the numerator and denominator of the above equation with I, we get a relation between L and KE as,
`KE=(1)/(2)(I^(2) omega^(2))/(I)=(1)/((I omega)^(2))/(I)`
`KE=(L^(2))/(2I)`
As `KE==(L^(2))/(2I) i.e., KE prop L^(2)`. It resembles with `y=Kr^(2)`. If angular momentum is same for two objects, kinetic energy is inversely proportional to moment of inertia.
`:.` Moment of inertia of the object whose kinetic energy is lesser will have greater magnitude