a). nuclear
No. There were batteries long long before we learned
how to use nuclear energy. Also, there is no danger of
exposure to radioactivity when you're working with a battery.
b). mechanical
No. A battery has no moving parts.
c). gravitational
No. No matter how high you take a battery in an airplane, or
how far you lower it into a mine-shaft, its characteristics don't
change. In fact, batteries even work on things that are in orbit.
d). chemical
Bingo.
