What is the gravitational field strength at a distance of 3R from the center of

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Question: What is the gravitational field strength at a distance of 3R from the center of the Earth? (R = radius of the Earth) (2022)

Options:

Correct Answer: g/9

Exam Year: 2022

Solution:

Gravitational field strength decreases with the square of the distance. At 3R, it is g/9.

What is the gravitational field strength at a distance of 3R from the center of the Earth? (R = radius of the Earth) (2022)

What is the gravitational field strength at a distance of 3R from the center of the Earth? (R = radius of the Earth) (2022)

Step 1: Understand that 'R' is the radius of the Earth.
Step 2: Recognize that the gravitational field strength (g) at the surface of the Earth is a certain value.
Step 3: Know that gravitational field strength decreases with the square of the distance from the center of the Earth.
Step 4: Calculate the distance from the center of the Earth at 3R, which is 3 times the radius of the Earth.
Step 5: Use the formula for gravitational field strength: g' = g / (distance^2). Here, distance = 3R.
Step 6: Substitute the distance into the formula: g' = g / (3R)^2.
Step 7: Simplify the equation: g' = g / (9R^2).
Step 8: Since g at the surface is g, at 3R it becomes g/9.

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