Question

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

Answer 1

Potential energy and the total mechanical energy of a body may be negative. Kinetic energy is always positive.

If total mechanical energy equals zero, it is possible $P.E.=-K.E.$

Since $K.E.\ne 0,momentum\ne 0$

One such example is a rocket fired at exactly escape velocity(speed at which body escapes gravitational pull of earth).