Question

at what height above the Earth surface the acceleration due to gravity will be 1/9 of it's values at the Earth surface.given radius of the Earth r=400 km​

Answer 1

Correct question:-

At what height above the Earth's surface, the acceleration due to gravity will be 1/9 of it's value at the Earth's surface. Given Radius of Earth, r = 6400 km.

Answer:-

Required height is 2844.44km above the Earth's surface.

Explanation:-

We know the expression :-

g' = g(1 - 2h/Rₑ)

Where :-

• g' is the acceleration due to gravity at

the given height from Earth's surface.

• g is acceleration due to gravity at the

Earth's surface.

• h is given height.

• Rₑ is radius of the Earth.

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Now, according to the question :-

⇒ g' = g/9

Substituting values in the above equation, we get :-

⇒ g/9 = g(1 - 2h/6400)

⇒ g/9g = (1 - 2h/6400)

⇒ 1/9 = 6400 - 2h/6400

⇒ 6400 = 9(6400 - 2h)

⇒ 6400 = 57600 - 18h

⇒ -18h = 6400 - 57600

⇒ -18h = -51200

⇒ h = -51200/18

⇒ h = 2844.44 km