if the mass of earth is doubled without changing its size what have what will happen to our weight

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Gravity would get doubled but the mass would not be doubled
So increase in weight would also be double of the previous weight

Now, W'=m*2g
W'=2*mg, and mg is equal to W
Hence proved

Eg Weight is 60N and gravity is,for instance 10m/s^2
Therefore mass is 6kg
Now g=20m/s^2
Therefor increased weight =6*20=120N
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