Question

Imagine you are standing atop a ladder so tall that you are 3 times as far from Earth's center as compared to the surface. What would be your weight at the top, relative to your weight at the surface?

Answer 1

Weight will become
`(1)/(9)` times of previous weight

Step-by-step explanation:

Acceleration due to gravity is given by
`g=(GM)/(R^2)` , G is gravitational constant , M is mass of earth and R is the radius of the earth

From the relation we can see that

`g\propto(1)/(R^2)`

So
`(g_(top))/(g)=(3R^2)/(R^2)` ( As it is given that you are standing at 3 times as far from compared to earth center )

So
`g_(top)=(g)/(9)`

As weight of the body is
`w=mg` , mass is constant and in new case acceleration due to gravity becomes
`g_(top)=(g)/(9)` so weight will also become
`(1)/(9)` times of previous weight