Q 11-07-191JEE MainJEE Main 2019 (12 Apr, Shift 2)Easy
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 $\dfrac19$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)
Answer: (B) $\dfrac R2$
$g = \dfrac{GM}{R^2}$, so
$$\frac{g_p}{g_e} = \frac{M_p}{M_e}\left(\frac{R}{R_p}\right)^2 \Rightarrow \frac49 = \frac19\left(\frac{R}{R_p}\right)^2 \Rightarrow R_p = \frac R2$$
(This uses the given weight ratio and mass ratio; the remark about equal density is not needed.)
Solution by Sreeraj P, M.Sc Physics