Question

Can a body have momentum when its energy is negative?

Answer 1

Hint: In this question use the formula for kinetic energy of the body which is given by, $K.E. = \dfrac{{{p^2}}}{{2m}}$ where $K.E.$ represents kinetic energy and $p$ represents momentum.

Complete step-by-step answer:

As we know that energy of a system is the sum of potential energy and kinetic energy and this potential energy in a body is present due to the position of body and the kinetic energy in a body exists due to its motion and the formula for kinetic energy $ = \dfrac{{{p^2}}}{{2m}}$ where $p$ is momentum and $m$ is mass, here kinetic energy is showing a direct relationship with momentum means it increases as the square of momentum
And if energy is negative then formula is:
$
   - E = \dfrac{{{p^2}}}{{2m}} \\
  p = \sqrt { - 2mE} \\
$
It means that momentum of a body also exists if in case the energy of the body is negative.

Note: If a body has some kinetic energy it is understood that it must have some velocity therefore if velocity exist than momentum also must be present in the body because momentum is given by the product of mass and velocity and we know that mass of a body cannot be zero, so if in a case energy is negative then in that case also momentum must be there it will not be zero. For example in an atom, an electron has momentum though its energy is negative.