Question

suppose you are standing on a tall ladder if your distance from the center of the earth is 2R what will be your weight?

Answer 1

We know formula of Acceleration due to gravity at h height from the Earth's surface is given by g = g₀/(1 + h/R)²
Here, g₀ is the acceleration due to gravity on Earth's surface.
h is the height from the Earth's surface.
R is the radius of earth .

A/C to question,
My distance from the centre of earth is 2R
So, my distance from the surface of earth is 2R - R = R
∴ g = g₀/( 1 + 1/1)² = g₀/(2)² = g₀/4

Hence, acceleration will be 1/4th times of acceleration at Earth's surface.
Hence , weight of body at 2R distance from centre of earth will be 1/4th of weight of body at Earth's surface.

Answer 2

I think this question is not worded correctly.  On the surface of the Earth, you are at the radius of the Earth, and you have a certain weight.  At three times the radius of the Earth, your weight would be only 1/32 = 1/9 as much.  At FOUR times the radius of the Earth, your weight is 1/42 = 1/16 as much.