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 decreases by 4% and K decreases by 2%
D. g decreases by 2% and K decreases by 4%

Answer

B

Explanation

`g= (GM)/(R^(2))`
or `g prop (R^-2)`
`:. %` change in `g = (-2)`(`%`change in `R`)
`=(-2)(-2)=+4%`
Rotational kinetic energy,
`K = (L^2)/(2I)` …………(i)
`L =` angular momentum `=` constant
`I= (2)/(5mR^2)` …………..(ii)
From Eqs. (i) and (ii),
`K prop (R^-2)`
`:. %`change in `K = (-2)`(`%` change in `R`)
`=(-2)(-2) = +4 %`.