Answer
For two objects of the same kinetic energies, the momentum will be directly proportional to the square root of their masses. They will have the same momentum only when the masses are equal.
Work Step by Step
As ratio of kinetic energy is given by: $E_2/E_1=2m_2.p_1^2/p_2^2.2m_1$
From problem
$E_1=E_2$
so Equation becomes
$p_1/p_2=\sqrt m_1/\sqrt m_2$.
So they will have the same momentum only when the masses are equal.
