The radius of plant 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 of its value on A ?

Explanation

Data : `R_(A)=R_(B)//2, g_(B)=(1)/(2)g_(A), M_(B)=?`
`g(GM)/(R^(2)) therefore g_(A)=(GM_(A))/(R_(A)^(2)) and g_(B)=(GM_(B))/(R_(B)^(2))`
`therefore (g_(B))/(g_(A))=((M_(B))/(M_(A)))((R_(A))/(R_(B)))^(2)`
`therefore (1)/(2)=((M_(B))/(M_(A)))((1)/(2))^(2)=(1)/(4)((M_(B))/(M_(A)))`
`therefore (M_(B))/(M_(A))=(4)/(2)=2`
`therefore M_(B)=2M_(A)`.