question_answer

If the density of the planet is double that of the earth and the radius 1.5 times that of the earth, the acceleration due to gravity on the planet is (a) \[\frac{4}{3}\]times that on the surface of the earth (b) 3 times that on the surface of the earth (c) \[\frac{3}{4}\]times that on the surface of the earth (d) 6 times that on the surface of the earth

Answer:

\[{{\rho }_{p}}={{r}_{p}}=1.5\,\,{{\rho }_{e}};\frac{{{g}_{p}}}{{{g}_{e}}}=?\] \[\Rightarrow \frac{{{g}_{p}}}{{{g}_{e}}}=\frac{{{\rho }_{p}}}{{{\rho }_{e}}}\times \frac{{{r}_{p}}}{{{r}_{e}}}=2\times 1.5=3\Rightarrow \,\,{{g}_{p}}=3{{g}_{e}}\]