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If the radius of the Earth shrinks by 2%...

If the radius of the Earth shrinks by `2%`, mass remaing same, then how would the have of acceleration due to gravity change?

Text Solution

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`g=(Gm^2)/(R^2)`
Taking logarithm `log g = log G+2log m-2log R`
Differenntiating it `(dg)/(g)=0+0-2(dR)/(R )= -2[(-2)/(100)]`
`(dg)/(g)xx100= -2[(-2)/(100)]xx100=4%`.
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