Effect of earth shrinking on acceleration due to gravity – Rankers Physics

Acceleration Due to Gravity and its variation: Practice Problem & Solution

If the radius of the earth were to shrink by one percent, its mass remaining the same, the value of \(g\) on the earth’s surface would
increase by 0.5%
increase by 2%
decrease by 0.5%
decrease by 2%

Solution Explained:

To solve this problem, we apply the core principles of Acceleration Due to Gravity and its variation. Understanding the underlying formula is key to arriving at the correct answer below:

Since \(g = \frac{GM}{R^2}\), differentiating gives \(\frac{dg}{g} = -2 \frac{dR}{R}\). A -1% change in R leads to a +2% change in g.

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