Correct option is (2) \(\sqrt {2}\) times
We know that
The kinetic energy in terms of the momentum and mass of the body is,
\(\Rightarrow E = \frac {p^2}{2m}\)
\(\Rightarrow E \propto P^2\)
When the energy of the body becomes twice its initial value, let E1 is the initial kinetic energy, and E2 is the final kinetic energy,
\(\Rightarrow \frac {E_1}{E_2} = \frac {p^2_1}{p^2 _2}\)
\(\Rightarrow \frac {1}{2} = \frac {p ^2 _1}{p^2 _2}\)
\(\Rightarrow \frac {1}{\sqrt {2}} = \frac {p_1}{p_2}\)
\(\Rightarrow p_2 = \sqrt {2}p_1\)
Thus, we conclude that if the kinetic energy of a body becomes twice its initial value then the new momentum of the body will be \(p_2 = \sqrt {2}\, p _1.\)
