The radii of two planets are `R_1 and R_2` and their densities are `rho_1 and rho_2` respectively. Then find ratio of acceleration due to gravity on the planets.

Options

A. `r_2/r_1 .(rhop_1)/(rho_2)`
B. `(r_2rho_2)/(r_1rho_1)`
C. `r_1/r_2 .(rhop_2)/(rho_1)`
D. `(r_1rho_1)/(r_2rho_2)`

Answer

B

Explanation

`implies g = (Gm)/r^2 = G/r^2 xx4/3 pir^3 rho " " [ :. m = 4/3pir^3rho]`
`:. G = 4/3 piGr rho `
`:.g prop r rho " " [ :. 4/3 pi G " constant "]`
`:. (g_2)/(g_1) = (r_2rho_2)/(r_1rho_1)`