Question

Weight of earth surface is w then its value at height.r (r=radius of earth

Answer 1

Given, weight at earth surface is W
Let acceleration due to gravity on Earth's surface is g₀
acceleration due to gravity at h from the Earth's surface is given by
g = g₀/(1 + h/r)²
∵ weight = mass × acceleration due to gravity
so, W is directly proportional to acceleration due to gravity.
now, Let weight at height h is W'
∴ W/W' = g₀/g₀/(1 + h/r)²
W' = W/(1 + h/r)²

Hence, weight at height h is W/(1 + h/r)²

Answer 2

Let W be the weight on Earth Surface.
Acceleration due to gravity on earth's surface be g₀
Relation between g and G
g= GM/R²

Variation of g with height h is :

gh=GM/(R+h)² 
 gh= (g₀R²/M)xM /(R+h)²
gh=g₀R²/(R+h)²
gh=g₀/(1+h/R)²----------------1

As we know that W=mxg
W is directly propositional to g

Let weight at height h be W1
∴W/W1= g₀/g₀/(1+h/R)²

W1=W/(1+h/R)²

∴Weight Of earth surface at height H is W/(1+h/R)²