imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth is size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g', then find the relation between g and g'.

Explanation

The acceleration due to gravity on the new planet can be found using the relation
`g = (GM)/(R^(2))`….(i)
But `M=4//3 piR^(3)rho,rho` being.
Thus, Eq. (i) becomes
`g=(Gxx(4//3)piR^(3)rho)/(R^(2))=Gxx(4)/(3)piR rhorArr g prop R" "(because rho="constant")`
`:. (g')/(g)=(R')/(R)rArr (g')/(g)=(3R)/(R)`
`rArr (g')/(g)=3rArr g'=3g`.