Question

Find ratio of the accelerations due to gravity of 2 planets if their radii ratio is 2 : 3. Under condition 

1. Mass remains constant 

2. Material remains constant.

Answer 1

1. Here since mass remains constant, g ∝\(\frac {M}{R^2}\) ⇒ g ∝1/R² 

⇒ Ratio of gravitation is,

\(\frac{g_1}{g_2}\) = \((\frac{R_2}{R_1})^2 \) = \(\frac {9}{4}\)

2. Here since material is same its density is same 

⇒ g ∝ ρR ⇒ g ∝ R