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