The radius of the 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 alueof g on B is half that of its value on A?

Explanation

Given `R_(A)=1/2R_(B):.(R_(A))/(R_(B))=1/2`
`g_(B)=1/2g_(a),:.(g_(B))/(g_(A))=1/2`
To find: Mass of planet B, `M_(B)=?`
Formula : `g=(GM)/(R^(2))`
Solution: For planet A
`g_(A)=(GM_(A))/(R_(A)^(2))`……..i
`g_(B)=(GM_(B))/(R_(B)^(2))`........ii
Dividing equation ii by i
`(g_(B))/(g_(A))=(GM_(B))/(R_(B)^(2))-:(GM_(A))/(R_(A)^(2))`
`(g_(B))/(g_(A))=(GM_(B))/(cancel(R)_(B)^(2))xx(R_(A)^(2))/(GM_(A))`
`(g_(B))/(g_(A))=(M_(B))/(M_(A))xx[(cancel(R)_(A))/(R_(B))]^(2)`
`1/2=(M_(B))/(M_(A))xx1/4`............. from given
`(cancel(4)^(2))/(cancel(2)_(1))=(M_(B))/(M_(A)):.2M_(A)=M_(B)`
`M_(B)=2M_(A)`
The mass of B is twice mass of A