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

`g=(GM)/(R^(2))=(Grho(4)/(3)piR^(3))/(R^(2))impliesg=(4)/(3)GrhopiR`
`impliesgpropRimplies(g)/(g')=(R)/(3R)impliesg'=3g`