# If the kinetic energy of a body becomes four times, its momentum will become:

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If the kinetic energy of a body becomes four times, its momentum will become:
1. three times its initial. value
2. four times its initial value
3. two times its initial value
4. remains unchanged

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Correct Answer - Option 3 : two times its initial value

CONCEPT:

• Kinetic energy (K.E): The energy possessed by a body by the virtue of its motion is called kinetic energy.

The expression for kinetic energy is given by:

$KE = \frac{1}{2}m{v^2}$

Where m = mass of the body and v = velocity of the body

• Momentum (p): The product of mass and velocity is called momentum.

Momentum (p) = mass (m) × velocity (v)

The relationship between the kinetic energy and Linear momentum is given by:

As we know,

$KE = \frac{1}{2}m{v^2}$

Divide numerator and denominator by m, we get

$KE = \frac{1}{2}\frac{{{m^2}{v^2}}}{m} = \frac{1}{2}\frac{{\;{{\left( {mv} \right)}^2}}}{m} = \frac{1}{2}\frac{{{p^2}}}{m}\;$ [p = mv]

$\therefore KE = \frac{1}{2}\frac{{{p^2}}}{m}\;$

$p = \sqrt {2mKE}$

CALCULATION:

Given that:

The kinetic energy of body becomes 4 times,

final momentum (p'):

$p' = \sqrt {2mKE} = \sqrt {2m \times 4KE} = 2 \times \sqrt {2mKE} = 2p$