Question

The value of g at the surface of the earth is 9.8 m/s2. Then the value of g at the place 480 km above the surface of the earth will be nearly? (Radius of the earth is 6400 km)
1. 9.8 m/s2
2. 7.2 m/s2
3. 8.5 m/s2
4. 4.2 m/s2
plz explain

Answer 1

M = mass of earth

R = radius of earth = 6400 km = 6.4 x 10⁶ m

g₁ = acceleration due to gravity on the surface of earth = 9.8 m/s²

h = height above the surface of earth = 480 km = 0.480 x 10⁶ m

g₂ = acceleration due to gravity above the surface of earth = ?

acceleration due to gravity on the surface is given

g₁ = GM/R²                                                   eq-1

acceleration due to gravity above the surface is given

g₂ = GM/(R + h)²                                                   eq-2

dividing eq-2 by eq-1

g₂ /g₁ = (GM/(R + h)²) /(GM/R² )

g₂ /g₁ = R²/(R + h)²

inserting the values

g₂ /9.8 = (6.4 x 10⁶)²/((6.4 x 10⁶) + (0.480 x 10⁶))²

g₂ = 8.5 m/s²