Let g be the acceleration due to gravity at the earth's surface and K the rotational kinetic energy of the earth. Suppose the earth's radius decreases by 2%. Keeping all other quantities constant, then

Options

A. `g` increases by 2% and `K` increases by 2%
B. `g` increases by 4% and `K` increases by 4%
C. `g` increases by 4% and `K` increases by 2%
D. `g` increases by 2% and `K` increases by 4%

Answer

B

Explanation

`g=(GM)/(R^(2)),K=(1)/(2)Iomega^(2)=(L^(2))/(2l)`
Further, `L` will remain constant.
`therefore" "Kprop(1)/(I)orKprop(1)/((2)/(5)MR^(2))`
`or" "KpropR^(-2)andgpropR^(-2)`