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. $2 W$
• 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 $