Two planets A and B of radii R and 1 . 5   R have densities ρ and ρ 2 respectively. The ratio…

Two planets A and B of radii R and 1.5 R have densities ρ and ρ2 respectively. The ratio of acceleration due to gravity at the surface of B to A is:
  1. 2 : 3
  2. 2 : 1
  3. 3 : 4
  4. 4 : 3

Solution

The acceleration due to gravity is 

g=GMR2=4πGRρ3⇒g∝ρ·R

Thus, the ratio is 

⇒gBgA=1.5Rρ2ρR=12×1.5=0.75⇒gBgA=34

Asked in: JEE Main 2023 (13 Apr Shift 2)

Practice more Gravitation questions on Aicharya