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Question

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)


A
The ratio of the acceleration due to gravity on them is 1:15
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B
For the same volume of planets, the mass of planet A is greater than that of planet B.
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C
A body weighs 15 times more on planet B than on planet A.
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D
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.
$$R_A:R_B=2:5, D_A:D_B=1:6$$
$$\displaystyle g_A:g_B=\dfrac {\dfrac {GM_A}{R_A^2}}{\dfrac {GM_B}{R_B^{2}}}=\dfrac {4}{3}\pi \dfrac {R_A^3D_A}{R_A^2}\times \dfrac {R_B^2}{\dfrac {4}{3}\pi R_B^3d_B}=\dfrac {R_Ad_A}{R_Bd_B}$$
$$\dfrac {g_A}{g_B}=\dfrac {2}{5}\times \dfrac {1}{6}=\dfrac {1}{15}$$
$$W_B=mg_B=15mg_A=15W_A$$
For the same volume of planets, mass of planet A is $$1/6$$ the mass of planet B.
Planet B has a greater volume than planet A.

Physics

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