Q. A body weight 63 N on the surface of the earth. What is the gravitational force on it due to the earth at a height of 3200 Km from the surface of the earth? [Radius of the earth is 6400 Km]

Soln:

Weight on the earth's surface (We) = 63 N

Radius of the earth (R) = 6.4 * 10⁶ m

Height from earth's surface (h) = 3200 Km = 3200000 Km = 3.2 * 10⁶ m

Let M is the mass of the earth and G is the gravitational constant. Then, the weight of the body on the earth is

We = mg = m * (GM/R²)

When the body is at a height h from the earth's surface, the weight of the body is

Wh = mg' = m * [GM/(R + h)²]

∵ Wh/We = R² / (R + h)² = [R/(R + h)]²

Wh = [ 6.4 * 10⁶ / (6.4 * 10⁶ + 3.2 * 10⁶ ) ]² * 63 = 28 N Ans.

Hence, the required gravitational force on it due to earth is 28 N.