# If a body of mass M has momentum P, then Kinetic Energy will be _______?

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If a body of mass M has momentum P, then Kinetic Energy will be _______?
1. P2 / m
2. P2 / 2m
3. m2 / 2P
4. P / 2m

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Correct Answer - Option 2 : P2 / 2m

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)

EXPLANATION:

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]

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