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If the gravitational field strength at the top of Mount Everest is 9.772 N/kg, approximately how tall (in feet) is
the mountain?

Respuesta :

Answer:

The height of the Everest mountain is, x =  8514.087 m

Explanation:

Given data,

The gravitational field strength at the top of mount Everest, gₓ = 9.772 m/s²

The formula for gravitational field strength is,

                                gₓ = GM/(R+x)²

Where, x is the height from the surface of the Earth

Therefore,

                                (R+x)² = GM/gₓ

                                     x = √(GM/gₓ) - R

Substituting the values,

                       x = √(6.67408 x 10⁻¹¹ X  5.972 x 10²⁴ / 9.772) - 6.378 x 10⁶

                       x =  8514.087 m          

Therefore, the height of the Everest mountain is, x =  8514.087 m                                                              

abidemiokin

The height of the Everest mountain is 8514.087 m  

Gravitational field strength

The gravitational field strength at the top of Mount Everest, gₓ = 9.772 m/s²

The formula for gravitational field strength is,

  • gₓ = GM/(R+x)²

Where:

x is the height from the surface of the Earth

Substituting the given parameters into the formula, we will have:

  • (R+x)² = GM/gₓ
  • x = √(GM/gₓ) - R

Substituting the values,

x = √(6.67408 x 10⁻¹¹ × 5.972 x 10²⁴/9.772) - 6.378 x 10⁶

x =  8514.087 m          

Therefore, the height of the Everest mountain is 8514.087m

Learn more on gravitational field strength here: https://brainly.com/question/14080810                                                        

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