A) The ratio of acceleration due to gravity on them is\[1:15\].
B) For the same volume of planets, mass of planet \[A\] is greater than that of planet\[B\].
C) A body weighs \[15\] times more on planet \[B\] than on planet\[A\].
D) Planet \[B\] has greater volume than planet\[A\].
Correct Answer: B
Solution :
\[{{R}_{A}}:{{R}_{B}}=2:5,\,\,{{D}_{A}}:{{D}_{B}}=1:6,\,\,{{g}_{A}}:{{g}_{B}}\] \[\frac{\frac{G{{M}_{A}}}{R_{A}^{2}}}{\frac{G{{M}_{B}}}{R_{B}^{2}}}=\frac{4}{3}\pi \frac{{{R}^{3}}_{A}{{D}_{A}}}{R_{A}^{2}}\times \frac{{{R}^{2}}}{\frac{4}{3}\pi R_{B}^{3}{{D}_{B}}}=\frac{{{R}_{A}}{{D}_{A}}}{{{R}_{B}}{{D}_{B}}}\] \[\frac{{{g}_{A}}}{{{g}_{B}}}=\frac{2}{5}\times \frac{1}{6}=\frac{1}{15}\] \[{{W}_{B}}=m\,\,{{g}_{B}}=15\,\,m\,\,{{g}_{A}}=15\,\,{{W}_{A}}\] For the same volume of planets, mass of planet \[A\] is \[1/{{6}^{th}}\] the mass of planet\[B\]. Planet \[B\] has greater volume than planet\[A\].
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