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)

$2^{1/3}W$ at the planet.

$\text{Since the density of planet is same as that of earth}$

${\rho }_p={\rho }_e$

$\Rightarrow \frac{M_p}{\frac{4}{3}\pi R_p^3}=\frac{M_e}{\frac{4}{3}\pi R_e^3}$

$\Rightarrow \frac{R_p}{R_e}=(\frac{M_p}{M_e}{)}^{1/3}$

The value of gravitational acceleration acceleration $=g=\frac{GM}{R^2}$

$\Rightarrow \frac{W_p}{W_e}=\frac{m{g}_p}{m{g}_e}$

$\Rightarrow \frac{g_p}{g_e}=\frac{M_p}{M_e}\frac{R_e^2}{R_p^2}$

$\Rightarrow \frac{M_p}{M_e}(\frac{M_e}{M_p}{)}^{2/3}$

$=(\frac{M_e}{M_p}{)}^{1/3}=2^{1/3}$

$\Rightarrow W_p=2^{1/3}W$ at the planet

Hence option D is correct