Question

At what height from the surface of the earth does the value of acceleration due to gravity be 2.45m/s square where the radius of the earth is 6400 km.​

Answer 1

Answer: 6,277,647m

Explanation:

Radius of Earth = 6400km

To calculate the gravitational acceleration of a planet, we use the following formula:

g = mG/r^2

Gravitational acceleration is equal to the mass of the planet multiplied by the gravitational constant all divided by the radius of the planet squared.

We already know what the gravitational acceleration will be, 2.45m/s^2.

So, 2.45m/s^2 = mG/r^2

the mass of the earth is equal to 5.9*10^24.

And the gravitational constant is equal to 6.67408 * 10^-11.

We don't know the radius though.

2.45m/s^2 = 5.9*10^24 * 6.67408 * 10^-11 divided by r^2

2.45m/s^2 = 3.93 * 10^14 divide by r^2

Now, we can cross-multiply.

2.45m/s^2 * r^2 = 3.93 * 10^14

divide r^2 from both sides.

r^2 = 3.93 * 10^14 divided by 2.45m/s^2

r^2 = 1.6*10^14.

Now, take the square root of both sides.

r = 12,677,647 meters from the center of the Earth.

To calculate the height from the surface of the Earth, we need to subtract r by the Earth's radius.

That will be 12,677,647-6.400.000m = 6,277,647m from the surface of Earth.