Ratio of gravitational force acting on body at height 1600 kilometre to gravitational force acting on the same body on the earth surface
Answers
Ratio of gravitational force acting on body at height 1600 kilometre to gravitational force acting on the same body on the earth surface is 16/25
Solution:
•Radius of earth is 6400km
•Gravitational force(F) = GMm/R²
•Force at surface = GMm/(6400)²
( F1) _____(1)
•Force at 1600km = abovethesurface
(F2) GMm/(6400+1600)²
_____(2)
•Divide (2) by (1)
F2/F1 = GMm/(8000)²
_____________
GMm/(6400)²
=>F2/F1 = (6400)²/(8000)²
= 4²/5²
= 16/25
The ratio between the two forces is 16/25.
Explanation:
- Height of body "h" = 1600 km
- Radius of earth = 6400 km
- Gravitational force(F) = GMm/R^2
Force at surface = GMm/(6400)^2 ( F1) -------(1)
Similarly
Force at 1600 km = above the surface
(F2) GMm / (6400+1600)^2 ------- (2)
Divide equation (2) by (1)
F2/F1 = GMm/(8000)^2 ÷ GMm/(6400)^2
F2/F1 = (6400)^2 / (8000)^2
= (4)²/(5)²
= 16/25
The ratio between the two forces is 16/25.