But, as @Christopher said, apparently not one dense or warm enough to support life as we know it. However, I'm no astrophysicist, so maybe it's still implausible anyway, I don't know...
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It's all implausible. Blowing apart the Earth would be immensely difficult -- it'd take something like the Sun's entire energy output for a week. And a mass as large as the surviving chunk would probably collapse into a sphere, though I don't know how long that would take. At least, it would probably have been put into a spin by the explosion rather than just hanging there.