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The ratio of the weights of a body on Earth's surface to that on the surface of a planet is 9:4. 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? (Take the planets to have the same mass density)
$$\frac{g_e}{g_p} = \frac{M_e}{M_p} \times \left(\frac{R_p}{R_e}\right)^2$$
$$\frac{9}{4} = 9 \times \left(\frac{R_p}{R}\right)^2 \implies \left(\frac{R_p}{R}\right)^2 = \frac{1}{4}$$
$$R_p = \frac{R}{2}$$
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