Question

If the Earth had twice its present radius and twice its present mass, what would happen to your weight? Explain

Answer 1

Your weight basically depends on the acceleration due to gravity(g) which is 9.8 m/s2.
g itself depends on the mass and radius of the earth given by:
\[g = \frac{ GM }{ r ^{2} }\]

Answer 2

where M: Mass of the earth
r: radius of earth.

Answer 3

Fiddly ... in the formula cited above by someone else, if you substitute 2M for M, and 2r for r, then you'd get G2M/(2r)^2=G2M/4r^2 = GM/2r^2. So, the value of g in the equation would be halved. So, the pull on you would be less, you'd feel less reaction on the ground, and so lighter, you lucky sausage.
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