Q: Does "head" have the same meaning in the following two sentences?

The head of the list.

I've got to go to the head.

A: different meanings

Q: Does "oblige" have the same meaning in the following two sentences?

We had to oblige him.

The singer obliged with another song.

A: the same meaning

Q: Does "dig" have the same meaning in the following two sentences?

Dig coal.

Dig out a channel.

A:
different meanings