If the mass of the Earth were to double and its radius were to be halved, the acceleration due to gravity on its surface would become how many times its present value?

C. 8 — Using the formula g = GM/R^2, substituting the new values gives g' = G(2M)/(R/2)^2 = 8GM/R^2. Thus, the new gravity is 8 times the original.

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$If the mass of the Earth M becomes 2 M and its radius R becomes R /2, the acceleration due to gravity g^{'} = \frac{G ( 2 M )}{( R /2 ) ^{2}} becomes how many times its present value g = \frac{GM}{R ^{2}} ?$

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Correct answer: C — $8$

Using g = \frac{GM}{R ^{2}}, the new gravity is g^{'} = \frac{G ( 2 M )}{( R /2 ) ^{2}} = \frac{2 GM}{R ^{2} /4} = 8 \frac{GM}{R ^{2}} = 8 g .