If Earth was flat as pancake, how thick should be the pancake in order to provide us with the same gravity?

Question

If raduis of round Earth is Re?

Answer 1

Sounds like a Bouguer plate
a=g=2pi*G*H*rho
9.8 m*sec^-2/2pi*6.67 × 10−11 N m^2 kg^−2=H*rho
H*rho=2.34x10^10 kg/m^2
rho=Mean density earth= 5,515.3 kg/m³ ......... ref Wikipedia
therefor
H=4.24x10^6 m
or
H=4.24 x 10^3 km

Interesting, thanks

Answer 2

OK, the question wants to provide US with the same gravity, which means that the inhabitants on the earth's surface feel the same effect.

Round earth: M = 4πρ/3 *R^3
Flat earth: M = πρ*R^2 T
For the masses to be equal, T = 4R/3

However, that will not give us the same gravity on the surface, but rather the same gravity in space.

Gravity on the surface = GM/r^2
Round earth: effect = 4πρ/3 *R
Flat earth: effect = πρ*R^2 T / (T/2)^2 = 4πρR^2 / T

For the effect to be the same T = 3R

*EDIT*
Let's consider the case where the radius of the flat earth is different from the radius of the round earth. But the mass and gravity are the same on the surface.

Round earth: Mass = 4*Re^3 / 3
Gravity = 4*R3 / 3

Flat earth: Mass = R^2 T
Gravity = 4R^2 / T

We require R^2 / T = R3 / 3
and R^2 T = 4Re^3 / 3

R^2 = 2Re^2 / 3
T = 2*Re

Answer 3

mmm...pancakes.

does it have syrup?

i have to have syrup with my pankcakes.

and maybe some strawberries...