The answer is option 'C': K.E. increases

Explanation:
When the shell is fired from a cannon, it possesses both kinetic energy (K.E.) and momentum. The explosion in mid-air causes a change in the shell's state, affecting its momentum and kinetic energy. Let's analyze the different factors involved:

1. Momentum:
Momentum is defined as the product of an object's mass and its velocity. In this case, the shell has both mass and velocity, and therefore possesses momentum before the explosion.

When the shell explodes in mid-air, it breaks apart into multiple fragments. According to the law of conservation of momentum, the total momentum of an isolated system remains constant unless acted upon by external forces.

Before the explosion, the shell's momentum is the sum of the momenta of all its fragments. After the explosion, the fragments continue to move, but their velocities and directions change. The total momentum of the system after the explosion is still conserved, but the distribution of momentum among the fragments is different. Therefore, the momentum of the shell may increase or decrease depending on the individual velocities and masses of the fragments.

2. Kinetic Energy:
Kinetic energy is the energy possessed by an object due to its motion. It depends on both the mass and velocity of the object.

Before the explosion, the shell has a certain amount of kinetic energy associated with its motion. When the explosion occurs, the fragments of the shell also possess kinetic energy due to their individual motions. As a result, the total kinetic energy of the system (shell + fragments) increases after the explosion.

This increase in kinetic energy is due to the fact that the explosion imparts additional motion to the fragments, resulting in an overall increase in the system's kinetic energy. Therefore, the correct answer is option 'C': K.E. increases.

To summarize, when a shell is fired from a cannon and explodes in mid-air, the total momentum of the system may change, but the total kinetic energy increases due to the additional motion imparted to the fragments by the explosion.