Question

When the momentum of a body is zero can kinetic energy be there or not.
Second part,
When the kinetic energy of a body is zero can momentum be there or not.
If yes then why if no then why?

Answer 1

Dear Student,

(1)
$$\begin{gathered} \mathrm{Momentum},\mathrm{p}=\mathrm{mass}\left(\mathrm{m}\right)\times \mathrm{speed}\left(\mathrm{v}\right) \\ \mathrm{Kinetic}\mathrm{Energy},\mathrm{KE}=\frac{1}{2}{\mathrm{mv}}^2 \\ \mathrm{or},\mathrm{KE}=\frac{{\mathrm{p}}^2}{2\mathrm{m}} \end{gathered}$$

It looks like the only way a body can have zero momentum is to have either zero mass or else zero speed, and if either of those is zero, then that makes the Kinetic Energy also zero as well, too.

So the answer to the question is no.

(2)
$$\begin{gathered} \mathrm{Momentum},\mathrm{p}=\mathrm{mass}\left(\mathrm{m}\right)\times \mathrm{speed}\left(\mathrm{v}\right) \\ \mathrm{Kinetic}\mathrm{Energy},\mathrm{KE}=\frac{1}{2}{\mathrm{mv}}^2 \\ \mathrm{or},\mathrm{KE}=\frac{{\mathrm{p}}^2}{2\mathrm{m}} \\ \mathrm{p}=\sqrt{\left(\mathrm{KE}\right)\times 2\mathrm{m}} \end{gathered}$$

Momentum is the product of mass and velocity of a body. If a body is in motion, obviously it should have kinetic energy. So, if a body has momentum, it possesses kinetic energy.

According to the above relation, if kinetic energy is zero then momentum is also zero.


Regards