Answer:
Weight will become [tex]\frac{1}{9}[/tex] times of previous weight
Explanation:
Acceleration due to gravity is given by [tex]g=\frac{GM}{R^2}[/tex] , G is gravitational constant , M is mass of earth and R is the radius of the earth
From the relation we can see that
[tex]g\propto\frac{1}{R^2}[/tex]
So [tex]\frac{g_{top}}{g}=\frac{3R^2}{R^2}[/tex] ( As it is given that you are standing at 3 times as far from compared to earth center )
So [tex]g_{top}=\frac{g}{9}[/tex]
As weight of the body is [tex]w=mg[/tex] , mass is constant and in new case acceleration due to gravity becomes [tex]g_{top}=\frac{g}{9}[/tex] so weight will also become [tex]\frac{1}{9}[/tex] times of previous weight
