what will be the value of g on the surface of the Earth if the mass was twice and its radius half was what is need now
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g=10m/s............2
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G would be eight times larger, since it is proportional to mass and inversely proportional to distance squared. [Thanks to Niels for pointing out an earlier mistake]
The Earth would need to be 16 times as dense, though, which is quite impossible. The density of rock is around 3 g/cm^3, of iron around 8 and the Earth overall (consisting mostly of those two materials, including compression) around 6. The densest known material is around 22 g/cm^3 (Osmium), which is only roughly 4 times as much. Even when you consider increased compression, no planet could possibly satisfy your conditions, even if it were made of pure Osmium.
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