Question

What will be acceleration due to gravity on the surface of the moon if its radius were `(1//4)^(th)` the radius of earth and its mass `(1//80)^(th)` the mass of earth? What will be the escape velocity on the surface of moon if it is `11.2 km//s` on the surface of the earth? (given that `g=9.8 m//s^(2)`)

Answer 1

`R_(m)=(R_(e))/4,M_(m)=(M_(e))/80`
`g_(e)=(GM_(e))/(R_(e)^(2)),g_(m)=(GM_(m))/(R_(m)^(2))`
`(g_(m))/(g_(e))=(M_(m))/(M_(e)).((R_(e))/(R_(m)))^(2)=1/80xx(4)^(2)=1/5`
`g_(m)=(g_(e))/5=9.8/5=1.96m//s^(2)`
`(v_(e))_(e)=sqrt((2GM_(e))/(R_(e))), (v_(e))_(m)=sqrt((2GM_(m))/(R_(m)))=sqrt((2GM_(e))/(80R_(e)//4))`
`=1/(sqrt(20)) v_(e)`
`(v_(e))_(m)=11.2/(sqrt(20))=2.5 km//s`