A shell explodes and many pieces fly in different directions. The following is conserved:
A) Kinetic energy
B) Momentum
C) Both
D) None

Hint:When a shell explodes, the initial energy is converted into different forms of energy.
Momentum of an object is formulated as, thus depends on both, mass of the object and its velocity.

Complete step by step answer:
When a shell explodes, it is divided into a number of pieces, which have unequal masses and fly with unequal velocities in different directions.
During this process, various energy changes occur and some amount of energy is also lost. Initial kinetic energy is, therefore, greater than the final kinetic energy thus we cannot say that the kinetic energy of the system is conserved. Hence, option A is incorrect.
This implies that option (C) is also incorrect.
We know, Conservation of momentum states that the amount of momentum of the system remains constant before and after explosion, as momentum can never be created nor be destroyed.
In this question, let us consider the shell of mass \[M\] and velocity \[V\] on explosion divides itself into 3 parts of masses \[{m_1}\], \[{m_2}\] and \[{m_3}\] having velocities \[{v_1}\], \[{v_2}\], \[{v_3}\]respectively.
Now, the momentum of an object is the product of its mass and velocity, so we can say initial momentum is equal to its final momentum and therefore,
\[MV = {m_1}{v_1} + {m_2}{v_2} + {m_3}{v_3}\]
This indicates that momentum is conserved.
Thus option (B) is correct.
This implies option (D) is also incorrect.

Option (B) Momentum is the correct answer.

Note: In the collision of an isolated system, momentum is always conserved. This same principle of conservation of momentum is also applicable in the case of rockets. It gives out gases in the backward direction, and by conservation of momentum, the rocket attains a forward momentum that enables it to move forward.