Question

The radius of planet A is half the radius of planet B. If the mass of A is M_A, what must be the mass of B so that the value of g on B is half that of its value on A?

Answer 1

Radius of planet ‘A’ = R_A, radius of planet ‘B’ = R_B 
Mass of planet ‘A’ = M_A, mass of planet ‘B’ = M_B = ? 
From given... 

`R_A = (R_B)/2; g_B = 1/2 g_A`

`g = (GM)/(R^2)`

`∴ g_A = (GM_A)/(R_A^2)`

`∴ g_B = (GM_B)/(R_B^2)`

`(GM_B)/(R_B^2)`

`(GM_B)/(R_B^2)  = 1/2((GM_A)/((RB/2)^2))`

`(GM_B)/(R_B^2)  = 1/2 (4(GM_A)/((R_B)^2))`

Cancel out G and `R_B^2` from both sides

`M_B = 1/2(4M_A)`

`M_B = 2 M_A`

∴ The mass of planet B must be twice the mass of planet A.