Inside Report (2)

What do you do with a worn-out nuclear submarine? The US Navy is expected to announce by the end of the month that it will begin studies on the effect of scuttling more than 100 nuclear subs in the Atlantic and Pacific Oceans. Prime locations for such ''dumping'': off California's Cape Mendocino and North Carolina's Cape Hatteras.

California state Sen. Barry Keene says the Navy has indicated it ''could take years'' to begin the sub-disposal plan. But he cites a Science magazine report that a single submarine could contain more than half as much radioactivity as all the nuclear waste the US has dumped offshore over a period of more than 20 years.

Keene wants President Reagan to ban radioactive dumping off California and propose an international treaty to stop all such dumping in the Pacific.