Correct Answer  Option 2 : P
^{2} / 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]
\(\therefore KE = \frac{1}{2}\frac{{{p^2}}}{m}\;\)