The acceleration due to gravity g on earth is $9.8{ \mathrm{ms}}^{-2}$. What would the value of g for a planet whose size is the same as that of earth but the density in twice that of earth?

Volume of earth $\left(V\right)=\frac{4\pi }{3}{R}^3$. Therefore, density of earth is $\rho =\frac{M}{V}$ or $M=V\rho =\frac{4\pi }{3}{R}^3\rho$
Now $g=\frac{GM}{R^2}=\frac{4\pi G\rho R}{3}$. Since R is the same for both planets, if $\rho$ is doubled, the value of g is also doubled. Hence the correct choice is (1).