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(B) Given,mass of the second planet $M_2 = 8 M_1$,where $M_1$ is the mass of the first planet.Since the density $\rho$ is the same for both planets,we

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$2$

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(B) Given,mass of the second planet $M_2 = 8 M_1$,where $M_1$ is the mass of the first planet.Since the density $ho$ is the same for both planets,we have $M = \frac{4}{3} \pi R^3 ho$.Thus,$M \propto R^3$,which implies $R \propto M^{1/3}$.Therefore,$\frac{R_2}{R_1} = \left(\frac{M_2}{M_1}ight)^{1/3} = (8)^{1/3} = 2$,so $R_2 = 2 R_1$.The acceleration due to gravity is given by $g = \frac{GM}{R^2}$.The ratio of the acceleration due to gravity of the second planet to that of the first planet is:$\frac{g_2}{g_1} = \frac{M_2}{M_1} 	imes \left(\frac{R_1}{R_2}ight)^2$Substituting the values,we get $\frac{g_2}{g_1} = 8 	imes \left(\frac{1}{2}ight)^2 = 8 	imes \frac{1}{4} = 2$.Thus,the ratio is $2$.

Consider two spherical planets of same average density. The second planet is $8$ times as massive as the first planet. The ratio of the acceleration due to gravity of the second planet to that of the first planet is

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