Question

Two planets A and B have their radii in the ratio 2:52:5 respectively

• A. The ratio of the 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

Answer 1

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

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 greater volume than planet A

Here, ratio of volumes is $\frac{V_A}{V_B}=\frac{R_A^3}{R_B^3}=(2/5{)}^3=8/125<1$ so, $V_A<V_B$

The ratio of acceleration, $\frac{g_A}{g_B}=\frac{\left(G{M}_A/R_A^2\right)}{\left(G{M}_B/R_B^2\right)}=\left(R_B/R_A{)}^2\right({\rho }_A{V}_A/{\rho }_B{V}_B)=(25/4\left)\right(1/6\left)\right(8/125)=1/15$