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

Options

A. decrease by 2%
B. increased by 2%
C. incresed by 4%
D. decrease by 4%

Answer

C

Explanation

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%`