The answer (like many other scientific answers) depends on the dose - or in this case, the power of the nuke.
For example, according to one set of simulations, a small nuke wouldn't be enough since the asteroid would "reassemble" from blown-apart chunks:
Don Korycansky of the University of California, Santa Cruz, and Catherine Plesko of the Los Alamos National Laboratory in New Mexico simulated blowing up asteroids 1 kilometre across. When the speed of dispersal was relatively low, it took only hours for the fragments to coalesce into a new rock.
However, a big enough explosion may do the job:
"It (the asteroid) would be blown to smithereens," said study lead author Bob Weaver of Los Alamos National Laboratory in New Mexico, who presented the findings here Dec. 13 at the fall meeting of the American Geophysical Union.
"There was a lot of back-of-the-envelope stuff," he told SPACE.com. By contrast, Weaver said, he and his colleagues developed sophisticated codes to model exactly what would happen in such an explosion.
In previous studies, the researchers had modeled how a nuke would affect a solid asteroid about 1,650 feet (500 meters) long and with a shape based on a known oblong space rock called Itokawa.
That work found that a nuke could blast the asteroid into pieces too small to pose much danger. And the explosion would send these pieces flying apart at tremendous speeds - fast enough that they would not re-aggregrate to threaten the Earth again.
In the new study, the researchers modified their codes. The size of the asteroid remained the same, at 1,650 feet long, but now the researchers stipulated that it was 25 percent porous. It was attacked with a 500-kiloton nuclear blast - about 20 to 30 times more powerful than the U.S. blast inflicted on Nagasaki, Japan, to help end World War II.
The researchers exploded the nuke on the space rock's surface, as in previous models. And once again, the asteroid was blown to tiny, harmless bits that spread outward too quickly to be drawn back together. The best results were achieved by positioning the explosive on the asteroid's short side, Weaver said, but any orientation they tried did the job.