Question

The ratio of the weights of an object on the Earth's surface to that on the surface of a planet is $9:4$ where both planets have same density. The mass of the planet is $\frac{1}{9}$ th of that of the Earth. If R' is the radius of the Earth, what is the radius of the planet?

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

Answer 1

Answer: (D)

$w_{1}=\frac{GM_{1} m}{R_{1}^{2}}$
$w_{2}=\frac{GM_{2} m}{R_{2}^{2}}$
$\frac{w_{1}}{w_{2}}=\frac{M_{1}}{M_{2}}\left(\frac{R_{2}}{R_{1}}\right)^{2}$
$\frac{4}{9}=\frac{1}{9}\left(\frac{R_{2}}{R_{1}}\right)^{2}$
$\frac{R_{1}}{R_{2}}=\frac{1}{2}$