If the radius of the Earth is R, what is the gravitational acceleration at a hei

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Question: If the radius of the Earth is R, what is the gravitational acceleration at a height R above the Earth\'s surface?

Options:

Correct Answer: g/4

Solution:

At a height R above the Earth\'s surface, the gravitational acceleration is g/4, derived from the formula g\' = g(R/(R+h))^2.

If the radius of the Earth is R, what is the gravitational acceleration at a height R above the Earth's surface?

If the radius of the Earth is R, what is the gravitational acceleration at a height R above the Earth's surface?

Step 1: Understand that 'g' is the gravitational acceleration at the Earth's surface.
Step 2: Know that the radius of the Earth is represented as 'R'.
Step 3: Recognize that 'h' is the height above the Earth's surface, which in this case is equal to 'R'.
Step 4: Write down the formula for gravitational acceleration at a height 'h': g' = g(R/(R+h))^2.
Step 5: Substitute 'h' with 'R' in the formula: g' = g(R/(R+R))^2.
Step 6: Simplify the expression: g' = g(R/(2R))^2.
Step 7: Further simplify: g' = g(1/2)^2.
Step 8: Calculate (1/2)^2, which equals 1/4.
Step 9: Therefore, g' = g/4, meaning the gravitational acceleration at a height R above the Earth's surface is g/4.

Gravitational Acceleration – Understanding how gravitational acceleration changes with distance from the center of the Earth.
Height Above Earth's Surface – Calculating gravitational effects at a specific height above the Earth's surface.
Inverse Square Law – Applying the inverse square law to gravitational force and acceleration.