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

Hint:For a system total energy is the stored energy which a body is having from initial, and the energy during motion which is converted from the stored one. Also from the second law of motion states that the time rate of change of momentum is equal to the force acting on the particle.

Complete step by step solution:
Yes, an object can have momentum even when its mechanical energy is zero because Mechanical energy is the sum of potential energy and the Kinetic energy
i.e.,
Mechanical Energy (M.E) = Potential energy (P.E) + Kinetic Energy (K.E)
M.E = 0
So, K.E + P.E = 0
P.E = -K.E
Like this,

It has some kinetic energy. It means that the body has motion.

Hence,

Even if its mechanical energy is zero, the body has momentum.

The potential energy and total mechanical energy of a body can be negative. Kinetic energy is always positive.

Mechanical energy comprises both potential energy and kinetic energy. Momentum is zero which means velocity is zero. Hence, there is no kinetic energy but the object may possess potential energy.

Additional Information:Conservation of energy, according to which the energy of interaction of body or particles in a closed system is constant. The first type of energy that was identified was kinetic energy or energy of motion. In some collisions of particles, called elastic, the sum of the kinetic energy of the particles before the collision is equal to the sum of the kinetic energy of the particles after the collision. The notion of energy was progressively widened to include other forms. The kinetic energy lost by the body traveling upward against the force of gravity was thought to be converted into potential energy, or stored energy, which in turn is converted to kinetic energy.



Notes:Momentum is mass in motion, and any moving object can have momentum. The change in the momentum of an object is equal to its momentum. Impulse is the amount of force multiplied by the time interval. The momentum is not equal to the momentum itself rather, it is an increase or decrease in the amount of motion of an object.