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?

Explanation

Given : `R_(A)=(1)/(2)R_(B),g_(B)=(1)/(2)g_(A)`
To find : Relation between masses of A and B
Formula : `g=(Gm)/(R^(2))`
Solution :
`g_(A)=(GM_(A))/(R_(A)^(2))andg_(B)=(GM_(B))/(R_(B)^(2))`
`(g_(A))/(g_(B)) = ((GM_(A))/(R_(A)^(2)))/((GM_(B))/(R_(B)^(2)))`
`(g_(A))/(g_(B)) = (M_(A))/(M_(B)) xx (R_(B)^(2))/(R_(A)^(2))`
`(g_(A))/((1)/(2) g_(A)) = (M_(A))/(M_(B)) xx (R_(B)^(2))/(((1)/(2) R_(B))^(2)) ` (as given)
`2 = (M_(A))/(M_(B)) xx 4`
`(2)/(4) = (M_(A))/(M_(B))`
`M_(B) = 2 M_(A)`