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Three planets of same density and with radii $R_{1}, R_{2} and R_{3}$ such that $R_{1} = 2 R_{2} = 3 R_{3}$ have gravitational fields on the surface $g_{1}, g_{2}, g_{3}$ and escape velocity $v_{1}, v_{2} and v_{3}$ respectively then

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$\frac{g_{1}}{g_{2}} = \frac{1}{2}$

$\frac{g_{1}}{g_{3}} = 3$

$\frac{v_{1}}{v_{2}} = 2$

$\frac{v_{1}}{v_{2}} = \frac{1}{3}$

answer is B, C.

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Detailed Solution

$g = \frac{4}{3} πGRρ, v_{e} = R \sqrt{\frac{8}{3} πGρ}$

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