Question

Best relationship between momentum and kinetic energy possessed by an object in terms of mass is

• A. $momentum={(2m\times kineticenergy)}^{\frac{1}{2}}$
• B. ${\left(momentum\right)}^{\frac{1}{2}}=2m\times kineticenergy$
• C. ${\left(Kineticenergy\right)}^{\frac{1}{2}}=2\times momentum$
• D. $Kineticenergy={(2\times momentum)}^{\frac{1}{2}}$

Answer 1

The correct option is A

$momentum={(2m\times kineticenergy)}^{\frac{1}{2}}$

Step 1: Expression of kinetic energy and momentum

Kinetic energy (K.E) = $\frac{1}{2}m{v}^2$

Momentum (p) = $mv$

where $m$ = mass and $v$ = velocity

Step 2: Relation between momentum and kinetic energy

Considering the expression of kinetic energy,

$K.E=\frac{1}{2}m{v}^2$

Multiplying mass $\left(m\right)$ on numerator and denominator,

$$\begin{gathered} K.E=\frac{1}{2}m{v}^2\left(\frac{m}{m}\right) \\ K.E=\frac{m^2{v}^2}{2m} \\ K.E=\frac{{\left(mv\right)}^2}{2m} \end{gathered}$$

Substituting $mv=p$,

$$\begin{gathered} K.E=\frac{p^2}{2m} \\ 2mxK.E=p^2 \\ p={(2mxK.E)}^{\frac{1}{2}} \end{gathered}$$

Therefore $momentum={(2m\times kineticenergy)}^{\frac{1}{2}}$

Hence the correct answer is Option A.