Question

Consider a planet in some solar system which has a mass double the mass of the earth and density equal to the average density of the earth. An object weighing $W$ on the earth will weigh

• A. $W$
• B. $2W$
• C. $W/2$
• D. $2^{1/3}W$ at the planet

Answer 1

Answer: (D)

$M_p=\rho \cdot \frac{4}{3}\pi R_p^3$
$M_e=\rho \cdot \frac{4}{3}\pi R_e^3$
$\frac{l_p}{l_e}=\frac{G{M}_p/R_p^2}{G{M}_e/R_e^2}$
$=\frac{M_p}{M_e}\cdot \frac{R_e^2}{R_p^2}=\left(\frac{M_p}{M_e}\right){\left(\frac{M_e}{M_p}\right)}^{2/3}$
$={\left(\frac{M_p}{M_e}\right)}^{1/3}=(2{)}^{1/3}$
$\frac{W_p}{W_e}=\frac{m{g}_p}{m{g}_e}=(2{)}^{1/3}$
$W_p=(2{)}^{1/3}{W}_e=(2{)}^{1/3}W$