• # question_answer Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g', then A) $g'=3g$B)  $g'=\frac{g}{9}$C) $g'=9g$D) $g'=27g$

The acceleration due to gravity on the new plan can be found using the relation $g=\frac{GM}{{{R}^{2}}}$ but $M=\frac{4}{3}\pi {{R}^{3}}\rho ,\rho$being density. Thus, Eq. (i) becomes $\therefore$ $g=\frac{G\times \frac{4}{3}\pi {{R}^{3}}\rho }{{{R}^{2}}}$ $=G\times \frac{4}{3}\pi R\rho$ $\Rightarrow$$g\propto R$ $\therefore$ $\frac{g'}{g}=\frac{R'}{R}$ $\Rightarrow$$\frac{g'}{g}=\frac{3R}{R}=3$ $\Rightarrow$$g'=3g$