Question

The ratio of the weights of a body on the Earth’s surface to that on the surface of a planet is $9:4$. The mass of the planet is ${\left(\frac{1}{9}\right)}^{\text{th}}$ of that of the Earth. If $R$ is the radius of the earth, what is the radius of the planet ? (Take the planets to have the same mass density).

• A. $\frac{R}{2}$
• B. $\frac{R}{3}$
• C. $\frac{R}{4}$
• D. $\frac{R}{9}$

Answer 1

The correct option is A $\frac{R}{2}$

Given that

$\frac{W_e}{W_p}=\frac{m{g}_e}{m{g}_p}=\frac{9}{4}$

$\Rightarrow \frac{g_e}{g_p}=\frac{9}{4}$

Now, $g=\frac{GM}{R^2}$

$\Rightarrow \frac{g_e}{g_p}=\frac{\frac{GM}{R^2}}{G\left(\frac{M}{9}\right)R_p^2}=\frac{9}{4}$

$\therefore R_p=\frac{R}{2}$.

Hence, $\left(D\right)$ is the correct answer.