How does K.E. of an object change if its momentum is doubled?

We have,

(K.E.)₁= P²/2m

Where ‘P’ is momentum and ‘m’ is the mass of the object.
If the momentum is doubled then,

(K.E.)₂ = (2P)²/2m

Or, (K.E.)₂ = 4(K.E.)₁

Therefore, on doubling the momentum, the K.E. of the body increases by four times its initial K.E.