what are the drugs they use when they put someone into a medicaly induced coma?

Question

also what part of the brain is damaged when someone goes into a coma

Answer 1

Drug induced comas are done with barbiturates. They reduce cerebral activity, so the brain requires less oxygen, and reduce cerebral blood flow, so that brain swelling will go down. It's a last-ditch effort that is used when everything else (hyperventilation, steroids, diuretics, draining spinal fluid, decompressive surgery) has failed.

There are serious side effects, because the drugs cause severe cardiovascular depression. The patient must be on a ventilator, and is prone to pneumonia, as well.

Comas (not induced) may be due to anatomic lesions that cause the cerebral cortex or brain stem to malfunction, or by a lack of oxygen or glucose to the brain. Prolonged seizures can lead to coma, as can excess levels of toxins, such as ammonia, carbon dioxide or ketones.

Answer 2

Such medicines are called General anesthetics.
Anesthetics suppress cerebral cortex.