What would be the value of g on the surface of the earth if its mass was twice and its radius half of what it is now ?

Explanation

Given: `M'=2M`
`R'=R/2`
To find: `g=?`
Formula: `g=(GM)/(R^(2))`
Solution `g'=(GM')/(R^('2))`
`=(Gxx2M)/((R/2)^(2))=(Gxx2M)/((R^(2))/4)=(4xx2xxGM)/(R^(2))`
`therefore g' = 8g = 8xx 9.8`
`therefore g= 78.4 m//s^2` i.e., 8 times the original value of g