Correct Answer  Option 4 : √2 times
CONCEPT:

Momentum: A property of a body in motion that is equal to the product of the body's mass and velocity is called momentum.
P = mv
where P is the momentum of the body, m is the mass of the body, and v is the velocity of the body.

Kinetic energy: The energy in a body due to its motion, is known as kinetic energy.
The kinetic energy in terms of momentum is given by:
\(K=\frac{P^2}{2m}\)
where K is the kinetic energy of the body, P is the momentum of the body and m is the mass of the body.
CALCULATION:
Given that the Kinetic energy of the body increased 2 times. 2K1 = K2
2K1 = K2
\(2\times\frac{P_1^2}{2M}=\frac{P_2^2}{2M}\)
\(\frac{P_2^2}{P_1^2}=\frac{2}{1}\)
P2 = √2 P1
So the correct answer is option 4.