If the radius of the earth were to decrease by 1% keeping it’s mass same, how

If the radius of the earth were to decrease by 1% keeping it’s mass same, how will the acceleration due to gravity change?

Posted by: - Andre
Posting Time: - 7/22/2015 2:05:45 AM
Subject: - Physics

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Best 5 Answers:-

Answer by:- Smith

Let the mass and radius of the earth be M and R respectively.
Acceleration due to gravity, g = GM/R^2
When the radius, R’ = R-R/100 = 99R/100 = 0.99R
So, the acceleration due to gravity, g’ = GM/(0.99R)^2
or, g’ = 1.02GM/R^2
Now, the change in acceleration due to gravity,
=g’ – g
=(1.02-1)GM/R^2
= (0.02)GM/R^2
Thus, the acceleration due to gravity increases by 2%.

 
   

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