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(A) The relation between kinetic energy $(K)$ and momentum $(p)$ is given by $K = \frac{p^2}{2m}$,where $m$ is the mass of the body.Taking the natural

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(A) The relation between kinetic energy $(K)$ and momentum $(p)$ is given by $K = \frac{p^2}{2m}$,where $m$ is the mass of the body.Taking the natural logarithm on both sides:$\ln K = \ln \left( \frac{p^2}{2m} \right)$$\ln K = \ln(p^2) - \ln(2m)$$\ln K = 2 \ln p - \ln(2m)$Rearranging the terms to express $\ln p$ in terms of $\ln K$:$2 \ln p = \ln K + \ln(2m)$$\ln p = \frac{1}{2} \ln K + \frac{1}{2} \ln(2m)$This equation is of the form $y = mx + c$,where $y = \ln p$,$x = \ln K$,the slope $m = \frac{1}{2}$,and the intercept $c = \frac{1}{2} \ln(2m)$.Since the slope is positive and constant,the graph of $\ln p$ versus $\ln K$ is a straight line.

Which of the following graphs represents the graphical relation between momentum $(p)$ and kinetic energy $(K)$ for a body in motion?

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