Question

A body weighs 100 N on the surface of earth. At what height above the surface of earth will it weigh 50 N?​

Answer 1

Given:-

→ Weight of the body at the surface

of earth = 100N

To find:-

→ Height above the surface of earth, at which the body will weigh 50 N.

Solution:-

• Radius of the earth = 6400km

Let the required height be 'h' km.

Weight at a height of 'h' km :-

=> Wₕ = mgₕ

= mg(R/R + h)²

[ ∵ gₕ = g(R/R + h)² ]

Now :-

• mg = 100N

• R = 6400km

• Wₕ = 50N

=> 50 = 100[R/R + h ]²

=> 50/100 = [R/R + h ]²

=> 0.5 = [R/R + h]²

=> √0.5 = √[R/R + h ]²

=> 0.707 = R/R + h

=> 0.707R + 0.707h = R

=> 0.707h = R - 0.707R

=> 0.707h = 0.293R

=> h = 0.293×6400/0.707

=> h = 2652.33 km

Thus, at a height of 2652.33 km above the surface of earth, the body will weigh 50N.