If both the mass and the radius of the earth decrease by 1%, the value of the acceleration due to gravity will


let mass of earth be M, Radius be R

​For Acceleration due to gravity 'g', we have g=GM/R² 

Where G is Universal Gravitational Constant.

If mass of earth is decreased by 1% then , decreased mass let M' would be,

M'=M-M/100
​M'=99M/100
​where M/100 is 1% of actual Mass.

In the same way for decreased radius be R'
R'=R-R/100 
​R'=99R/100

​Let the Acceleration due to gravity when mass and radius decreased by 1% be g'

Now g'=GM'/(R')²
         g'=G x 99M/100
                 (99R/100)²
          g'=G x M
                99R²/100
          g'=100GM
                 99(R)²
          g'=100 x GM
​​                 99      R²
          g'= 100/99 g
          g'=(1.0101....)g
         

This would be the change in acceleration due to gravity. 

  • 14
What are you looking for?