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

Options

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

Answer

D

Explanation

`implies` We know that g ` = (GM)/R^2`
Mass `M = rho (4/3 piR^3)` , wehre `rho ` = Density
`:. G = (G(4/3 pi R^3)rho)/(R^2)`
`:. G = 4/3 pi Grrho`
`("For new planet ")/("For earth")=(g.)/(g) =(4/3piGR.rho)/(4/3piGRrho)`
For new planent `R. = 3R`
`(g.)/g=(3R)/(R) = 3`
`:. g. = 3g`