Imagine a new planet having the same density as that of earth but `3` times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is `g` and that on the new plane is `g` , then :

Options

A. `g'=3g`
B. `g'=g/9`
C. `g'=9g`
D. `g'=27g`

Answer

A

Explanation

The acceleration due to gravity on the new planet can be found using the relation
`g=(GM)/(R^(2))`
but `M=4/3 piR^(3) rho, rho` being density.
Thus, Eq (i) becomes
`:. g=(Gxx4/3piR^(3)rho)/(R^(2))`
`=Gxx4/3 piRrho`
`implies g propR`
`:. (g')/g=(R')/R`
`implies (g')/g=(3R)/R=3`
`implies g'=3g`