Question

A body of mass m is moving with velocity v. If P is the momentum associated with the body and K.E is the kinetic energy. Then K.E and P are related as:

• A. K.E. =
• B. K.E. =
• C. K.E. =
• D. K.E. =

Answer 1

The correct option is A

K.E. =

Kinetic energy, $(K.E.)=\frac{1}{2}m{v}^2$ ................... (i)
Momentum, $\left(P\right)=mv$ ....................(ii)
Dividing and multiplying equation (i) by m, we get
$K.E.=\frac{{mv}^2}{2m}$ ....................(iii)
Now, substituting the value of P from eq (ii) in eq (iii), we get,
$K.E.=\frac{P^2}{2m}$