Question

if the density of a planet is doubled without any chance in its radius how does g changes on the planet

Answer 1

Let g be the earth's gravity.

And g° be the gravity on the Denser earth.

Density is given by

Density = Mass / Volume

Gravity on earth is calculated from the formula

F = GM/r^2

Since the volume isn't changing(r is constant) the mass must become double if the density becomes double.Therefore,

g° = G(2M)/r^2

g° = 2g

Thus gravity increases by 2 times

Answer 2

g=GM/R²...........(1)
where G,M,R are the universal gravitational constant, mass and radius of the planet
Then M=4/3(πR³)×p,where p=density of the earth.
..
Then, g' be the new g of the planet.
Moreover M'=8/3(πR³×p).
so, g'=G(8/3πR³p)/R².........(2)
also ,from (1), g=G(4/3πR³×p)/R²........(3)
Dividing, (3) by (2), we have,
g/g'=1/2=>g'=2g.