At what elevation above the Earth's surface is the acceleration due to gravity 1% less than it is at the surface? The radius of the Earth is 6.37 * 10⁶ m.

Question

Quizplus · Accepted Answer

The acceleration due to gravity decreases with increasing distance from the Earth's surface according to the formula:

g = GM/(r^2)

where g is the acceleration due to gravity, G is the gravitational constant, M is the mass of the Earth, and r is the distance from the Earth's center.

We want to find the height, h, at which the acceleration due to gravity is 1% less than it is at the surface. That is:

g(h) = 0.99 g(surface)

Using the formula above, we can write:

GM/(h^2) = 0.99 GM/(R^2)

where R is the radius of the Earth.

Simplifying and solving for h, we get:

h = R sqrt(0.99)

h = (6.37 x 10^6 m) sqrt(0.99)

h = 32.1 km

Therefore, the best choice is B.

At What Elevation Above the Earth's Surface Is the Acceleration