Question

Can any object have momentum even if its mechanical energy is zero? Explain

Answer 1

1. The sum of potential energy and the kinetic energy of the body is called mechanical energy.
2. $$\begin{gathered} M.E=K.E+P.E \\ giventotalmechanicalenergyiszeroso, \\ 0=K.E+P.E \\ \Rightarrow K.E=P.E=0 \\ \Rightarrow \frac{1}{2}m{v}^2=0 \\ \Rightarrow \frac{{\left(mv\right)}^2}{2m}=0 \\ \Rightarrow \frac{{\left(p\right)}^2}{2m}=0 \\ \Rightarrow p=0 \end{gathered}$$

Hence, when the mechanical energy is zero then the momentum is also zero.