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'.

Options

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

Answer

D

Explanation

`g=(GM)/(R^(2))=(G)/(R^(2)).(4)/(3)pi R^(3)rho = (4)/(3) G pi R rho`
where `rho` is the density and R is the radius of the earth.
As `(4)/(3)G. pi rho` is constant, `g prop R`.
Since the size of the new planet is 3 times the size of the earth. `therefore` Its radius will be 3R.
`therefore (g_(P))/(g_(E ))=(3R)/(R )=3`
`therefore g_(P)=3g_(E )` or `g_(P)=3g` or `g'=3g`