If the acceleration due to gravity on the surface of the earth is `9.8m//s^(2),` what will be the acceleration due to gravity on the surface of a planet whose mass and radius both are two times the corresponding quantities for the earth ?

Explanation

Data : `g_(e)=9.8m//s^(2), M_(p)=2M_(e)`,
`R_(p)=2R_(e),g_(p)=?`
Acceleration due to gravity, `g=(GM)/(R^(2))`
`therefore g_(e)=(GM_(e))/(R_(e)^(2)) and g_(p)=(GM_(p))/(R_(p)^(2))`
`therefore (g_(p))/(g_(e))=((M_(p))/(M_(e)))((R_(e))/(R_(p)))^(2)-2xx((1)/(2))^(2)=(1)/(2)`
`therefore g_(p)=(g_(e))/(2)=(9.8m//s^(2))/(2)=4.9m//s^(2)`
The acceleration due to gravity on the surface of the planet `=4.9m//s^(2)`.