Question: What is the value of gravitational acceleration at the height equal to the radius of the Earth?
Options:
g/2
g/4
g/3
g/8
Correct Answer: g/4
Solution:
At height R, g\' = g / (2^2) = g / 4.
What is the value of gravitational acceleration at the height equal to the radiu
Practice Questions
Q1
What is the value of gravitational acceleration at the height equal to the radius of the Earth?
g/2
g/4
g/3
g/8
Questions & Step-by-Step Solutions
What is the value of gravitational acceleration at the height equal to the radius of the Earth?
Step 1: Understand that gravitational acceleration (g) decreases with height above the Earth's surface.
Step 2: Know that the formula for gravitational acceleration at a height (h) above the Earth's surface is g' = g / (1 + h/R)^2, where R is the radius of the Earth.
Step 3: In this case, the height (h) is equal to the radius of the Earth (R), so we can substitute h with R in the formula.
Step 4: Substitute h = R into 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, so we have g' = g / 4.
Step 7: Conclude that the value of gravitational acceleration at the height equal to the radius of the Earth is g / 4.
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