Question

if the weight of the 4 kg mass on the surface of earth is 39.2N calculate the acceleration due to gravity of earth at height 32 km above the surface of the earth

Answer 1

Answer:

9.8m/s square

Explanation:

392/4=98

Answer 2

Given :

• Mass(m) = 4kg
• Weight of m on surface of earth = 39.2N

To find :

• Acceleration due to gravity at height 32 km above the surface of earth.

Solution :

• Let g₀ and g be the acceleration due to gravity at the surface of the earth and at height h above the surface respectively.

• We know that,

        Weight of an object on the surface of the earth = mg₀

     ∴ 39.2 = 4 × g₀

     ∴ g₀ = 9.8 m/s²

• Now, acceleration due to gravity at a height h above the surface of the earth is given by,

       g = g₀ ×  $(1-\frac{2h}{R} )$    where R is the radius of the earth

     ∴  $g = 9.8(1-\frac{2*32}{6400})$  

     ∴ $g = 9.8( 1 - 0.01)$

     ∴ $g = 9.702 m/s^{2}$

Answer  : The acceleration due to gravity of earth at height 32 km above the surface will be 9.702 m/s² .