Initial Momentum = Pi = mivi and,
Initilal Kinetic Energy = KE i = 1/2 mivi 2
Now, it is given that the momentum is doubled.
Thus, New Momentum = Pf = mfvf = 2Pi = 2mivi
From here, vf = 2mivi/mf
And, New Kinetic Energy = KEf = 1/2 mfvf 2 = 1/2 mf x (2mivi/mf)2 = 1/2 x 4 x mf/mf 2 x m i 2 vi2
= 2 x m2/m2 x mv i 2 = 2 mv i 2 = 4 x KE i
Note that mi = mf = m as mass doesn 't change in this case.
Thus, the kinetic energy becomes 4 times the initial.