Explanation:

When a charged object is placed on a solid piece of metal of irregular shape, the charge will distribute itself in such a way that the potential energy of the system is minimized. This can be understood by considering the properties of conductors and the concept of electrostatic equilibrium.

Properties of Conductors:
- Conductors are materials that allow the free movement of charges.
- In a conductor, charges reside on the surface and distribute themselves in such a way that the electric field inside the conductor is zero.
- The charges on the surface of the conductor will redistribute themselves until the electric potential is constant throughout the conductor.

Electrostatic Equilibrium:
- In electrostatic equilibrium, the net electric field inside a conductor is zero.
- If there were any excess charges inside the conductor, they would experience a force and move until the electric field is zero.
- In other words, charges will move to cancel out any electric field inside the conductor.
- This means that the charges will distribute themselves on the surface of the conductor in such a way that the potential energy of the system is minimized.

Explanation of Option A:
Option A states that the charge will distribute itself such that the potential energy of the system is minimized. This is the correct answer because in electrostatic equilibrium, the charges will distribute themselves on the surface of the conductor in such a way that the electric field inside the conductor is zero. This minimizes the potential energy of the system.

Explanation of Other Options:
- Option B states that the charge will distribute uniformly in the metal object. This is not necessarily true because the shape and composition of the object can affect the distribution of charges.
- Option C states that the charge will distribute itself such that total heat loss is minimized. This is not related to the distribution of charges in a conductor.
- Option D states that the charge will distribute uniformly on the surface of the object. This is partially true because the charges will distribute themselves on the surface, but it does not guarantee uniform distribution as it depends on the shape and composition of the object.

Therefore, the correct answer is option A, as the charges will distribute themselves on the surface of the conductor in such a way that the potential energy of the system is minimized.