If the radius of the earth was to shringk by 2% its mass remaining same the acceleraton due to gravity on the earth surface would be
If the radius of the earth was to shringk by 2% its mass remaining same the acceleraton due to gravity on the earth surface would be
A. decrease by 2%
B. increased by 2%
C. incresed by 4%
D. decrease by 4%
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Correct Answer - C
As `Gg=(GM)/(R^(2))` if R decreases then g increases taking logarithm of both the sides we get
`log g = log G+log M -2 log R`
Differentaiting it we get
`(dg)/(g)=0 +0-(2dR)/(r )=-2(-2)/(100)=(4)/(100)`
` therefore` % increasing in `g=(dg)/(g)xx100=4/100xx100=4%`
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