What is the acceleration due to gravity at a height equal to the radius of the E

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Question: What is the acceleration due to gravity at a height equal to the radius of the Earth?

Options:

Correct Answer: g/4

Solution:

At height equal to radius, g\' = g / (1 + h/R)² = g / (2)² = g/4.

What is the acceleration due to gravity at a height equal to the radius of the Earth?

What is the acceleration due to gravity at a height equal to the radius of the Earth?

Step 1: Understand that 'g' is the acceleration due to gravity at the surface of the Earth.
Step 2: Recognize that 'h' is the height above the Earth's surface, and in this case, it is equal to the radius of the Earth (R).
Step 3: Use the formula for gravity at a height: g' = g / (1 + h/R)².
Step 4: Substitute h with R in the formula: g' = g / (1 + R/R)².
Step 5: Simplify the equation: g' = g / (1 + 1)² = g / (2)².
Step 6: Calculate (2)², which is 4: g' = g / 4.
Step 7: Conclude that the acceleration due to gravity at a height equal to the radius of the Earth is g/4.

Gravitational Acceleration – Understanding how gravitational acceleration changes with height above the Earth's surface.
Height and Radius Relationship – Applying the relationship between height and the radius of the Earth to calculate changes in gravitational force.
Inverse Square Law – Recognizing that gravitational force decreases with the square of the distance from the center of the Earth.