A planet has twice the density of earth but the acceleration due to gravity on its surface is exactly the same as that on the surface of earth. Then, its radius in terms of the radius of earth (R) will be :

\(\frac{R}{2}\)

\(g = \frac{GM}{R^2}\)

\(g = \frac{G(\frac{4}{3}\pi R^3 \rho)}{R^2}\)

\(g = \frac{4}{3} \pi G \rho R\)

\(\frac{g_p}{g_e} = \frac{P_p}{P_e} \frac{R_p}{R_e}\)

\(\Rightarrow 1 = 2 \frac{R_p}{R_e}\)

\(\Rightarrow \frac{1}{2}\)

\(\Rightarrow R_p = \frac{R_e}{2}\)