# The kinetic energy of a body becomes two times of the initial value. The increase in momentum is _________.

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The kinetic energy of a body becomes two times of the initial value. The increase in momentum is _________.
1. 3 times
2. √3 times
3. 2 times
4. √2 times

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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.