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 $1:15$
• B. For the same volume of planets, the 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 a greater volume than planet A.

Answer 1

Answer: (A), (C), (D)

$R_A:R_B=2:5,D_A:D_B=1:6$
$g_A:g_B=\frac{\frac{G{M}_A}{R_A^2}}{\frac{G{M}_B}{R_B^2}}=\frac{4}{3}\pi \frac{R_A^3{D}_A}{R_A^2}\times \frac{R_B^2}{\frac{4}{3}\pi R_B^3{d}_B}=\frac{R_A{d}_A}{R_B{d}_B}$
$\frac{g_A}{g_B}=\frac{2}{5}\times \frac{1}{6}=\frac{1}{15}$
$W_B=m{g}_B=15m{g}_A=15W_A$
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.