Two planets A, B have their radii in the ratio $2 : 5$ and densities in the ratio $1 : 6$ respectively. Choose the correct statement(s)

The ratio of the acceleration due to gravity on them is

1 : 15

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For the same volume of planets, the mass of planet A is greater than that of planet B.

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A body weighs

15

times more on planet B than on planet A.

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Planet B has a greater volume than planet A.

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Solution

The correct options are
A The ratio of the acceleration due to gravity on them is $1 : 15$
C A body weighs $15$ times more on planet B than on planet A.
D Planet B has a greater volume than planet A.
$R_{A} : R_{B} = 2 : 5, D_{A} : D_{B} = 1 : 6$
$g_{A} : g_{B} = \frac{\frac{G M_{A}}{R_{A}^{2}}}{\frac{G M_{B}}{R_{B}^{2}}} = \frac{4}{3} π \frac{R_{A}^{3} D_{A}}{R_{A}^{2}} \times \frac{R_{B}^{2}}{\frac{4}{3} π R_{B}^{3} d_{B}} = \frac{R_{A} d_{A}}{R_{B} d_{B}}$
$\frac{g_{A}}{g_{B}} = \frac{2}{5} \times \frac{1}{6} = \frac{1}{15}$
$W_{B} = m g_{B} = 15 m g_{A} = 15 W_{A}$
For the same volume of planets, mass of planet A is $1 / 6$ the mass of planet B.
Planet B hasa greater volume than planet A.

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Two planets A, B have their radii in the ratio 2:5 and densities in the ratio 1:6 respectively. Choose the correct statement(s)

Two planets A, B have their radii in the ratio $2 : 5$ and densities in the ratio $1 : 6$ respectively. Choose the correct statement(s)