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' = 9g `
C. `g' = g/9`
D. `g' = 27g `

Answer

A

Explanation

Acceleration due to gravity on the surface of the earth is
` g = (G4/3 pi R^3 rho)/(R^2) = 4/3 pi GRrho`
where R is the radius and p is the density of the earth. Acceleration due to gravity on the surface of the new planet is
`g. = 4/3 pi G (3R) rho = 3g`