Question

Keeping the mass of the earth the same if thr Diameter of the earth is shrieked by 1%.what will be the percentage change in acceleration due to gravity on the surface.

Answer 1

We know the relation between gravity , mass of earth and the radius of earth.

g = G (Me) / (Re)²

Now , we are asked to find 'g' when 'Re' becomes 'Re - 1%Re' ( because size is shrunk by 1%, it becomes 99% of original). So after just fiting in the values, we have.

Let the new gravitational value be g'.

g' = G (6)( $10^{24}$ kg) / ( 99%) (6400000m)(99%)(6400000)

We have G value substituted. We have 6400000m= 64000 km

g' = (6.67)($10^{-11}$)(6)($10^{24}$) / 6336²

g' = (40.02)$10^{13}$ / 40144896

g' = 9.76 m/s²

Hence if the mass remained the same and the radius of earth became 99% or rather shrunk by 1 % , the new gravitational force we feel is 9.75 m/s².

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