What is the nature of the graph between momentum of a body and its kinetic energy?
What is the nature of the graph between momentum of a body and its kinetic energy?
Straight line
Parabola
Circle
Ellipse
Solution
Let the mass of the body be $m$ and velocity of the body be $v$, such that it has momentum $p$ and kinetic energy $E$.
Momentum, $p=m v$
$
\Rightarrow \quad p^2=m^2 v^2
$
Kinetic energy, $E=\frac{1}{2} m v^2$
$
\Rightarrow \quad E=\frac{p^2}{2 m}
$
Hence, the nature of the graph between momentum of a body and its kinetic energy is parabola.
i.e.,
$
E \propto p^2
$
